https://mathtest.chapman.edu/mathcs/api.php?action=feedcontributions&user=Jipsen&feedformat=atomMathChapman - User contributions [en]2021-09-28T13:10:14ZUser contributionsMediaWiki 1.35.1https://mathtest.chapman.edu/mathcs/index.php?title=MPC_Seminar&diff=31MPC Seminar2021-09-17T20:54:14Z<p>Jipsen: /* Thursday, September 23, 2021, 12:30 - 1:30 pm in AF 209C */</p>
<hr />
<div>This is the homepage of the Chapman University '''Mathematics, Physics, and Computation Seminars'''<br />
([[MPC Seminar]])<br />
<br />
''Seminar Organizers:'' Roman Buniy and Peter Jipsen<br />
<br />
<br />
== Fall 2021 ==<br />
<br />
The MPC seminar is held in-person in the '''Keck Center of Science and Engineering, Room 370''' (unless a speaker prefers to hold the talk over Zoom). The date and time are included in the announcements below.<br />
<br />
----<br />
----<br />
=== Thursday, September 23, 2021, 12:30 - 1:30 pm in AF 209C ===<br />
<br />
==== ''Speaker:'' '''Lev Vaidman, Tel Aviv University''' ====<br />
<br />
''Title:'' '''Counterfactual communication'''<br />
<br />
''Abstract:'' Possibility to communicate between spatially separated regions, without even a single photon passing between the two parties, is an amazing quantum phenomenon. The possibility of transmitting one value of a bit in such a way, the interaction-free measurement, was known for a quarter of a century. The protocols of full communication, including transmitting unknown quantum states were proposed only a few years ago, but it was shown that in all these protocols the particle was leaving a weak trace in the transmission channel, the trace larger than the trace left by a single particle passing through the channel. However, a simple modification of these recent protocols eliminates the trace in the transmission channel and makes all these protocols truly counterfactual.<br />
<br />
----<br />
<br />
== Spring 2021 ==<br />
<br />
<br />
=== Monday, May 3rd, 2021, 1 - 2 pm on Zoom ===<br />
<br />
==== ''Speaker:'' '''Simon Henry, University of Ottawa''' ====<br />
<br />
''Title:'' '''Localic C*-algebras and the Geometric Bohr topos'''<br />
<br />
''Abstract:'' The Bohr topos is a space attached to a C*-algebra A that has been introduced in the hope of producing a new point of view on the mathematics of Quantum mechanics. It is essentially the "space of commutative sub-C*-algebra of A". But its original construction had two problems: (1) it had "the wrong topology" and (2) it was a "non-geometric" construction, i.e. when applied to continuous families of C*-algebras, it wasn't compatible with certain change-of-base functors. In this talk I'll explain how the theory of localic C*-algebras and some classical idea from "geometric logic" allows to give a new version of this construction that solves both of these problems.<br />
<br />
''Link to paper:'' [https://arxiv.org/pdf/1502.01896.pdf arxiv.org/pdf/1502.01896.pdf]<br />
----<br />
<br />
<br />
=== Thursday, Jan 21st, 2021, 4 - 5 pm on Zoom ===<br />
<br />
==== ''Speaker:'' '''Mike Campbell, Eureka (SAP), joint work with Vernon Smith (Chapman University)''' ====<br />
<br />
''Title:'' '''An Elementary Humanomics Approach to Boundedly Rational Quadratic Models'''<br />
<br />
''Video of talk:'' [https://youtu.be/F74RlCAjC_A YouTube] ''Slides:'' [http://math.chapman.edu/~jipsen/seminarposters/MikeCampbell2021HumanomicsApproachBRQuadratic.pdf pdf]<br />
<br />
''Abstract:'' We take a refreshing new look at boundedly rational quadratic models in economics using some elementary modeling of the principles put forward in the book Humanomics by Vernon L. Smith and Bart J. Wilson. A simple model is introduced built on the fundamental Humanomics principles of gratitude/resentment felt and the corresponding action responses of reward/punishment in the form of higher/lower payoff transfers. There are two timescales: one for strictly self-interested action, as in economic equilibrium, and another governed by feelings of gratitude/resentment. One of three timescale scenarios is investigated: one where gratitude/resentment changes much more slowly than economic equilibrium ("quenched model"). Another model, in which economic equilibrium occurs over a much slower time than gratitude/resent evolution ("annealed model") is set up, but not investigated. The quenched model with homogeneous interactions turns out to be a non-frustrated spin-glass model. A two-agent quenched model with heterogeneous aligning (ferromagnetic) interactions is analyzed and yields new insights into the critical quenched probability p (1-p) that represents the empirical frequency of opportunity for agent i to take action for the benefit (hurt) of other that invokes mutual gratitude (resentment). A critical quenched probability p*i, i=1,2, exists for each agent. When p < p*i, agent i will choose action in their self-interest. When p > p*i, agent i will take action sensitive to their interpersonal feelings of gratitude/resentment and thus reward/punish the initiating benefit/hurt. We find that the p*i are greater than one-half, which implies agents are averse to resentful behavior and punishment. This was not built into the model, but is a result of its properties, and consistent with Axiom 4 in Humanomics about the asymmetry of gratitude and resentment. Furthermore, the agent who receives less payoff is more averse to resentful behavior; i.e., has a higher critical quenched probability. For this particular model, the Nash equilibrium has no predictive power of Humanomics properties since the rewards are the same for self-interested behavior, resentful behavior, and gratitude behavior. Accordingly, we see that the boundedly rational Gibbs equilibrium does indeed lead to richer properties.<br />
<br />
''Link to paper:'' [https://digitalcommons.chapman.edu/cgi/viewcontent.cgi?article=1330&context=esi_working_papers Chapman Digital Commons]<br />
<br />
== Spring 2020 ==<br />
<br />
The seminar talks are held in '''Keck Center for Science and Engineering, KC 370''' (Center St. Orange, CA 92866, intersection of Center St. And Sycamore St.), '''usually on Wednesday at 4 pm'''.<br />
Sometimes there will be a change of time or venue and the announcement will reflect this change.<br />
<br />
See [http://www.chapman.edu/about/maps-directions/index.aspx Maps<br />
and directions], Keck Center is Building 28 on the Campus Map [https://www.chapman.edu/about/_files/maps-and-directions/current-maps/campus-map.pdf <br />
Campus map]<br />
<br />
<br />
----<br />
----<br />
<br />
<br />
=== Friday, Feb 21st, 2020, noon - 1 pm in Keck 370, refreshments at 11:45 am (same room) ===<br />
<br />
==== ''Speaker:'' '''Christian Williams, University of California at Riverside''' ====<br />
<br />
''Title:'' '''Predicate Calculus for Algebraic Theories'''<br />
<br />
''Abstract:'' There is a notion of predicate for algebraic theories, which admits a calculus of both logical and algebraic operations. We thereby extend equational logic by first-order logic, and provide a natural type theory for algebraic structures.<br />
<br />
We demonstrate the idea with the theory of monoids, and derive the example predicate "prime". This and many algebraic examples are only useful when they are mapped from a theory into actual models. There is much to be done in this direction. However, the driving motivation of this work is the application to programming languages: we focus on applying the idea to a more general notion of theory with variable binding.<br />
<br />
The construction is given in the topos of presheaves on a theory T: a "predicate" is a sieve on an object t of T, which corresponds to a subfunctor of the representable T(-,t). For each type t, these predicates form a Heyting algebra, providing the constructors of intuitionistic logic. The operations of T can be lifted to act on predicates, and we construct a model Pred(T): T -->HeyAlg. The correspondence between the operations of T and those in the image of Pred(T) gives that the former are "polymorphic" with respect to the types of the latter. This process can be understood as providing the theory T with a polymorphic type system.<br />
<br />
The original motivation of this work is a logic for concurrency known as Namespace Logic. This applies to the reflective higher-order pi calculus, which is the language of the distributed computing platform RChain. We demonstrate the above framework by constructing namespace logic. This gives a glimpse into a large field of potential application.<br />
<br />
[http://math.chapman.edu/~jipsen/seminarposters/Christian_Williams_pcat_2020-02-21.pdf Slides from the talk]<br />
<br />
<br />
----<br />
----<br />
<br />
=== Wednesday, Feb 19th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Simon Cho, University of Michigan''' ====<br />
''Title:'' '''A categorical perspective on persistent and magnitude homology'''<br />
<br />
''Abstract:'' We define and explain both persistent homology and magnitude homology, and their respective roles in applications (in both pure and applied settings). We will exhibit how both arise as a "singular complex" of a metric space in essentially the same way, but for different values of a parameter.<br />
<br />
<br />
----<br />
----<br />
<br />
=== Wednesday, Feb 12th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Stephon Alexander, Brown University, Rhode Island''' ====<br />
''Title:'' '''The Quantum Cosmological Constant'''<br />
<br />
''Abstract:'' The mysteries surrounding the Cosmological Constant presides at the interface of quantum mechanics and gravity. In this seminar,<br />
I will provide a pedagogical discussion of the many faces of the cosmological constant problem and discuss some current research that<br />
paves new directions that invites us to rethink the quantum nature of vacuum energy.<br />
<br />
<br />
----<br />
----<br />
<br />
=== Tuesday, Jan 14th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Pedram Roushan, Google Inc., Santa Barbara, CA''' ====<br />
''Title:'' '''Quantum supremacy using a programmable superconducting processor'''<br />
<br />
''Abstract:'' The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor1. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 2^53 (about 10^16). Measurements from repeated experiments sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 seconds to sample one instance of a quantum circuit a million times—our benchmarks currently indicate that the equivalent task for a state-of-the-art classical supercomputer would take approximately 10,000 years. This dramatic increase in speed compared to all known classical algorithms is an experimental realization of quantum supremacy for this specific computational task, heralding a much-anticipated computing paradigm. If time permits, I will present some of our more recent measurements. <br />
<br />
<br />
----<br />
----<br />
<br />
<br />
<br />
== Previous Seminar talks ==<br />
<br />
* [[MPC Seminar 2019]]<br />
<br />
* [[MPC Seminar 2018]]<br />
<br />
* [[MathCS Seminar 2017]]<br />
<br />
* [[MathCS Seminar 2016]]<br />
<br />
* [[MathCS Seminar 2015]]<br />
<br />
* [[MathCS Seminar 2014]]<br />
<br />
* [[MathCS Seminar 2013]]<br />
<br />
* [[MathCS Seminar 2012]]<br />
<br />
* [[MathCS Seminar 2011]]<br />
<br />
* [[MathCS Seminar 2010]]<br />
<br />
* [[MathCS Seminar 2009]]<br />
<br />
* [[MathCS Seminar 2008]]<br />
<br />
* [[MathCS Seminar 2007]]<br />
<br />
* [[MathCS Seminar 2006]]<br />
<br />
* [[MathCS Seminar 2005]]<br />
<br />
* [[MathCS Seminar 2004]]<br />
<br />
* [[MathCS Seminar 2003]]<br />
<br />
* [[MathCS Seminar 2002]]</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=MPC_Seminar&diff=30MPC Seminar2021-09-17T20:41:57Z<p>Jipsen: </p>
<hr />
<div>This is the homepage of the Chapman University '''Mathematics, Physics, and Computation Seminars'''<br />
([[MPC Seminar]])<br />
<br />
''Seminar Organizers:'' Roman Buniy and Peter Jipsen<br />
<br />
<br />
== Fall 2021 ==<br />
<br />
The MPC seminar is held in-person in the '''Keck Center of Science and Engineering, Room 370''' (unless a speaker prefers to hold the talk over Zoom). The date and time are included in the announcements below.<br />
<br />
----<br />
----<br />
=== Thursday, September 23, 2021, 12:30 - 1:30 pm in AF 209C ===<br />
<br />
==== ''Speaker:'' '''Lev Vaidman''' ====<br />
<br />
''Title:'' '''Counterfactual communication'''<br />
<br />
''Abstract:'' Possibility to communicate between spatially separated regions, without even a single photon passing between the two parties, is an amazing quantum phenomenon. The possibility of transmitting one value of a bit in such a way, the interaction-free measurement, was known for a quarter of a century. The protocols of full communication, including transmitting unknown quantum states were proposed only a few years ago, but it was shown that in all these protocols the particle was leaving a weak trace in the transmission channel, the trace larger than the trace left by a single particle passing through the channel. However, a simple modification of these recent protocols eliminates the trace in the transmission channel and makes all these protocols truly counterfactual.<br />
<br />
----<br />
<br />
== Spring 2021 ==<br />
<br />
<br />
=== Monday, May 3rd, 2021, 1 - 2 pm on Zoom ===<br />
<br />
==== ''Speaker:'' '''Simon Henry, University of Ottawa''' ====<br />
<br />
''Title:'' '''Localic C*-algebras and the Geometric Bohr topos'''<br />
<br />
''Abstract:'' The Bohr topos is a space attached to a C*-algebra A that has been introduced in the hope of producing a new point of view on the mathematics of Quantum mechanics. It is essentially the "space of commutative sub-C*-algebra of A". But its original construction had two problems: (1) it had "the wrong topology" and (2) it was a "non-geometric" construction, i.e. when applied to continuous families of C*-algebras, it wasn't compatible with certain change-of-base functors. In this talk I'll explain how the theory of localic C*-algebras and some classical idea from "geometric logic" allows to give a new version of this construction that solves both of these problems.<br />
<br />
''Link to paper:'' [https://arxiv.org/pdf/1502.01896.pdf arxiv.org/pdf/1502.01896.pdf]<br />
----<br />
<br />
<br />
=== Thursday, Jan 21st, 2021, 4 - 5 pm on Zoom ===<br />
<br />
==== ''Speaker:'' '''Mike Campbell, Eureka (SAP), joint work with Vernon Smith (Chapman University)''' ====<br />
<br />
''Title:'' '''An Elementary Humanomics Approach to Boundedly Rational Quadratic Models'''<br />
<br />
''Video of talk:'' [https://youtu.be/F74RlCAjC_A YouTube] ''Slides:'' [http://math.chapman.edu/~jipsen/seminarposters/MikeCampbell2021HumanomicsApproachBRQuadratic.pdf pdf]<br />
<br />
''Abstract:'' We take a refreshing new look at boundedly rational quadratic models in economics using some elementary modeling of the principles put forward in the book Humanomics by Vernon L. Smith and Bart J. Wilson. A simple model is introduced built on the fundamental Humanomics principles of gratitude/resentment felt and the corresponding action responses of reward/punishment in the form of higher/lower payoff transfers. There are two timescales: one for strictly self-interested action, as in economic equilibrium, and another governed by feelings of gratitude/resentment. One of three timescale scenarios is investigated: one where gratitude/resentment changes much more slowly than economic equilibrium ("quenched model"). Another model, in which economic equilibrium occurs over a much slower time than gratitude/resent evolution ("annealed model") is set up, but not investigated. The quenched model with homogeneous interactions turns out to be a non-frustrated spin-glass model. A two-agent quenched model with heterogeneous aligning (ferromagnetic) interactions is analyzed and yields new insights into the critical quenched probability p (1-p) that represents the empirical frequency of opportunity for agent i to take action for the benefit (hurt) of other that invokes mutual gratitude (resentment). A critical quenched probability p*i, i=1,2, exists for each agent. When p < p*i, agent i will choose action in their self-interest. When p > p*i, agent i will take action sensitive to their interpersonal feelings of gratitude/resentment and thus reward/punish the initiating benefit/hurt. We find that the p*i are greater than one-half, which implies agents are averse to resentful behavior and punishment. This was not built into the model, but is a result of its properties, and consistent with Axiom 4 in Humanomics about the asymmetry of gratitude and resentment. Furthermore, the agent who receives less payoff is more averse to resentful behavior; i.e., has a higher critical quenched probability. For this particular model, the Nash equilibrium has no predictive power of Humanomics properties since the rewards are the same for self-interested behavior, resentful behavior, and gratitude behavior. Accordingly, we see that the boundedly rational Gibbs equilibrium does indeed lead to richer properties.<br />
<br />
''Link to paper:'' [https://digitalcommons.chapman.edu/cgi/viewcontent.cgi?article=1330&context=esi_working_papers Chapman Digital Commons]<br />
<br />
== Spring 2020 ==<br />
<br />
The seminar talks are held in '''Keck Center for Science and Engineering, KC 370''' (Center St. Orange, CA 92866, intersection of Center St. And Sycamore St.), '''usually on Wednesday at 4 pm'''.<br />
Sometimes there will be a change of time or venue and the announcement will reflect this change.<br />
<br />
See [http://www.chapman.edu/about/maps-directions/index.aspx Maps<br />
and directions], Keck Center is Building 28 on the Campus Map [https://www.chapman.edu/about/_files/maps-and-directions/current-maps/campus-map.pdf <br />
Campus map]<br />
<br />
<br />
----<br />
----<br />
<br />
<br />
=== Friday, Feb 21st, 2020, noon - 1 pm in Keck 370, refreshments at 11:45 am (same room) ===<br />
<br />
==== ''Speaker:'' '''Christian Williams, University of California at Riverside''' ====<br />
<br />
''Title:'' '''Predicate Calculus for Algebraic Theories'''<br />
<br />
''Abstract:'' There is a notion of predicate for algebraic theories, which admits a calculus of both logical and algebraic operations. We thereby extend equational logic by first-order logic, and provide a natural type theory for algebraic structures.<br />
<br />
We demonstrate the idea with the theory of monoids, and derive the example predicate "prime". This and many algebraic examples are only useful when they are mapped from a theory into actual models. There is much to be done in this direction. However, the driving motivation of this work is the application to programming languages: we focus on applying the idea to a more general notion of theory with variable binding.<br />
<br />
The construction is given in the topos of presheaves on a theory T: a "predicate" is a sieve on an object t of T, which corresponds to a subfunctor of the representable T(-,t). For each type t, these predicates form a Heyting algebra, providing the constructors of intuitionistic logic. The operations of T can be lifted to act on predicates, and we construct a model Pred(T): T -->HeyAlg. The correspondence between the operations of T and those in the image of Pred(T) gives that the former are "polymorphic" with respect to the types of the latter. This process can be understood as providing the theory T with a polymorphic type system.<br />
<br />
The original motivation of this work is a logic for concurrency known as Namespace Logic. This applies to the reflective higher-order pi calculus, which is the language of the distributed computing platform RChain. We demonstrate the above framework by constructing namespace logic. This gives a glimpse into a large field of potential application.<br />
<br />
[http://math.chapman.edu/~jipsen/seminarposters/Christian_Williams_pcat_2020-02-21.pdf Slides from the talk]<br />
<br />
<br />
----<br />
----<br />
<br />
=== Wednesday, Feb 19th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Simon Cho, University of Michigan''' ====<br />
''Title:'' '''A categorical perspective on persistent and magnitude homology'''<br />
<br />
''Abstract:'' We define and explain both persistent homology and magnitude homology, and their respective roles in applications (in both pure and applied settings). We will exhibit how both arise as a "singular complex" of a metric space in essentially the same way, but for different values of a parameter.<br />
<br />
<br />
----<br />
----<br />
<br />
=== Wednesday, Feb 12th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Stephon Alexander, Brown University, Rhode Island''' ====<br />
''Title:'' '''The Quantum Cosmological Constant'''<br />
<br />
''Abstract:'' The mysteries surrounding the Cosmological Constant presides at the interface of quantum mechanics and gravity. In this seminar,<br />
I will provide a pedagogical discussion of the many faces of the cosmological constant problem and discuss some current research that<br />
paves new directions that invites us to rethink the quantum nature of vacuum energy.<br />
<br />
<br />
----<br />
----<br />
<br />
=== Tuesday, Jan 14th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Pedram Roushan, Google Inc., Santa Barbara, CA''' ====<br />
''Title:'' '''Quantum supremacy using a programmable superconducting processor'''<br />
<br />
''Abstract:'' The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor1. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 2^53 (about 10^16). Measurements from repeated experiments sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 seconds to sample one instance of a quantum circuit a million times—our benchmarks currently indicate that the equivalent task for a state-of-the-art classical supercomputer would take approximately 10,000 years. This dramatic increase in speed compared to all known classical algorithms is an experimental realization of quantum supremacy for this specific computational task, heralding a much-anticipated computing paradigm. If time permits, I will present some of our more recent measurements. <br />
<br />
<br />
----<br />
----<br />
<br />
<br />
<br />
== Previous Seminar talks ==<br />
<br />
* [[MPC Seminar 2019]]<br />
<br />
* [[MPC Seminar 2018]]<br />
<br />
* [[MathCS Seminar 2017]]<br />
<br />
* [[MathCS Seminar 2016]]<br />
<br />
* [[MathCS Seminar 2015]]<br />
<br />
* [[MathCS Seminar 2014]]<br />
<br />
* [[MathCS Seminar 2013]]<br />
<br />
* [[MathCS Seminar 2012]]<br />
<br />
* [[MathCS Seminar 2011]]<br />
<br />
* [[MathCS Seminar 2010]]<br />
<br />
* [[MathCS Seminar 2009]]<br />
<br />
* [[MathCS Seminar 2008]]<br />
<br />
* [[MathCS Seminar 2007]]<br />
<br />
* [[MathCS Seminar 2006]]<br />
<br />
* [[MathCS Seminar 2005]]<br />
<br />
* [[MathCS Seminar 2004]]<br />
<br />
* [[MathCS Seminar 2003]]<br />
<br />
* [[MathCS Seminar 2002]]</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=MPC_Seminar_2019&diff=29MPC Seminar 20192021-09-17T20:40:34Z<p>Jipsen: </p>
<hr />
<div><br />
== Fall 2019 ==<br />
<br />
The seminar talks are held in '''Keck Center for Science and Engineering, KC 370''' (Center St. Orange, CA 92866, intersection of Center St. And Sycamore St.), '''usually on Wednesday at 4 pm'''.<br />
Sometimes there will be a change of time or venue and the announcement will reflect this change.<br />
<br />
See [http://www.chapman.edu/about/maps-directions/index.aspx Maps<br />
and directions], Keck Center is Building 28 on the Campus Map [https://www.chapman.edu/about/_files/maps-and-directions/current-maps/campus-map.pdf <br />
Campus map]<br />
<br />
<br />
----<br />
----<br />
<br />
=== Thursday, Dec 12th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Alí Guzmán Adán, Universiteit Gent, Belgium''' ====<br />
''Title:'' '''Pizzetti and Cauchy formulae for higher dimensional surfaces: a<br />
distributional approach'''<br />
<br />
''Abstract:'' In this talk, we study Pizzetti-type formulas for Stiefel<br />
manifolds and Cauchy-type formulas for the tangential Dirac operator<br />
from a distributional perspective. First, we illustrate a general<br />
distributional method for integration over manifolds in R^m defined by<br />
means of k equations. We apply this method to derive an alternative<br />
proof of the Pizzetti formulae for the real Stiefel manifolds<br />
SO(m)/SO(m-k). Besides, a distributional interpretation of invariant<br />
oriented integration is provided. In particular, we obtain a<br />
distributional Cauchy theorem for the tangential Dirac operator on an<br />
embedded (m-k)-dimensional smooth surface.<br />
<br />
<br />
----<br />
----<br />
<br />
=== Wednesday, Dec 11th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Arjendu K Pattanayak, Physics and Astronomy, Carleton College, Northfield, Minnesota''' ====<br />
''Title:'' '''Quantum entanglement and tunneling oscillations in a (few) many-body nonlinear spin system'''<br />
<br />
''Abstract:'' Quantum tunnelling permits recoherence or refocusing in real or phase space after the initial quantum state has seemingly delocalized, exhibiting so-called classically forbidden dynamics. For a nonlinearly interacting many-body spin system this interim state can be an entangled state. We report on recent results from investigations into this phenomenon for initially spin coherent pure states in the paradigmatic kicked top (vale Haake) system. This has a mixed regualar and chaotic phase space in the classical limit and exhibits the entanglement tunneling described above, including coherent dynamics between phase-space stability islands; here the interim state is maximally entangled. We map the dependence on various parameters including nonlinear spin and number of spins involved (focusing mostly on the remarkable special case N=4) using a metric that attempts to quantify the quality and rate of tunnelling. The calculations of tunneling rates using eigenvalues and eigenstates of the time evolution operator as a function of initial condition compared to classical space structures demonstrates several nontrivial ways in which quantum behavior transitions to classical as the size of the system grows.<br />
<br />
<br />
----<br />
----<br />
<br />
=== Wednesday, Dec 4th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Raphael Drumond, Universidade Federal de Minas Gerais, Brazil''' ====<br />
''Title:'' '''The basics of Quantum Darwinism (and its relationship with non-Markovianity)'''<br />
<br />
''Abstract:'' Some aspects of physical systems described by quantum <br />
mechanics, most notably the possibility of violating a Bell inequality, <br />
suggests (to some) or unavoidably implies (to others) that certain <br />
properties of microscopic systems, like the precise values of position <br />
and momentum of a fundamental particle, do not have an objective <br />
reality. This strongly contrasts with the objectivity of properties of <br />
everyday macroscopic systems like the (rough estimate of) position and <br />
momentum of a baseball. Now, how can this objectivity of the <br />
macroscopic world emerge from a theory where, apparently, not all <br />
aspects of physical systems are objective? The notion of quantum <br />
Darwinism, put forward and popularized by Wojciech Zurek, is a path in <br />
that direction. In this talk I will discuss the main ideas behind <br />
quantum Darwinism, explore it in some simple models, and briefly discuss <br />
its relationship (or the lack of it) with the notion of non-Markovianity <br />
of quantum dynamical systems.<br />
<br />
<br />
----<br />
----<br />
<br />
=== Thursday, Nov 21th, 2019, 12:30 - 1:30 pm in Keck 370, refreshments from 12:15 (same room) ===<br />
<br />
==== ''Speaker:'' '''Sandu Popescu, University of Bristol, UK''' ====<br />
''Title:'' '''Exploring the limits of no-backward-in-time signaling'''<br />
<br />
''Abstract:'' One of the most routine observations that we make about our world is that we cannot signal backwards in time. So ubiquitous is this understanding that it is often taken as one of the basic laws of Nature. At first glance, this remark seems straightforward. However, as I will show, in probabilistic theories such as quantum mechanics, the consequences of such an assertion are far more involved. In fact, we will see that there is a surprising amount of liberty: some theories even allow the future to affect the past, nevertheless without signaling backwards in time.<br />
<br />
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<br />
=== Friday, Nov 8th, 2019, 3 - 4 pm in Keck 171, refreshments from 2:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Fredrik Dahlqvist, University College London, UK''' ====<br />
<br />
''Title:'' '''A probabilistic approach to floating point arithmetic'''<br />
<br />
''Abstract:'' Finite-precision floating point arithmetic introduces rounding errors which are traditionally bounded using a worst-case analysis. However, worst-case analysis might be overly conservative because worst-case errors can be extremely rare events in practice. Here we develop a probabilistic model of rounding errors with which it becomes possible to quantify the likelihood that the rounding error of an algorithm lies within a given interval. <br />
<br />
Given an input distribution, the model requires the distribution of rounding errors. We show how to exactly compute this distribution for low precision arithmetic. For high precision arithmetic we derive a simple but surprisingly useful approximation. The model is then entirely compositional: given a numerical program written in a simple imperative programing language we can recursively compute the distribution of rounding errors at each step and propagate it through each program instruction. This is done by applying a formalism originaly developed by Kozen to understand the semantics of probabilistic programs, for example how probability distributions gets transformed by assignments or "if then else" statements.<br />
<br />
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<br />
=== Wednesday, Nov 6th, 2019, 4 - 5 pm in Keck 370, refreshments from 3:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Jacques Pienaar, International Institute of Physics in Natal, Brazil''' ====<br />
<br />
''Title:'' '''The new question in quantum foundations: what is causality?'''<br />
<br />
''Abstract:'' Work in quantum foundations has tended to concentrate on Bell's Theorem, <br />
but recently a particular aspect of that theorem has taken on a life of <br />
its own: the question of what "causality" means in quantum mechanics, <br />
and how to model it. This movement has been driven in large part by <br />
recent advances in causal modeling in the statistical and Artificial <br />
Intelligence communities, which have had a heavy influence on quantum <br />
causal modeling. These "classical" approaches tend to define causality <br />
as a probabilistic and action-centered concept, which fits well with <br />
modern information-theoretic treatments of quantum mechanics. However, <br />
the classical approaches also tend to emphasize notions of underlying <br />
determinism and objective mechanisms that do not sit so well in the <br />
quantum context. In this talk I will step back from most of the <br />
technical jargon and try to get to the heart of some of the conceptual <br />
issues involved in "quantizing" the concept of causality, critically <br />
reviewing some key findings, pointing out potential inconsistencies and <br />
outlining possible directions for further inquiry into this fascinating <br />
problem.<br />
<br />
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<br />
=== Friday, October 18th, 2019, 12 - 1 pm in Keck 370, refreshments from 11:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Prof. Lev Vaidman, Alex Maguy-Glass Chair in Physics of Complex Systems, Tel Aviv University, Israel''' ====<br />
<br />
''Title:'' '''The past of a quantum particle'''<br />
<br />
''Abstract:'' Textbooks of quantum mechanics lack the concept of the past of quantum systems. Few years ago I proposed to define the past of a quantum particle according to the trace it leaves. While in many cases this definition provides a reasonable description, for a nested Mach-Zehnder interferometer it leads to a picture seemingly contradicting common sense: the particle leaves a trace in a place through which it could not pass. I will discuss recent theoretical and experimental studies of this controversial issue.<br />
<br />
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<br />
=== Friday, October 11th, 2019, 1 - 2 pm in Keck 370, refreshments from 12:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Prof. Thomas Curtright, University of Miami''' ====<br />
<br />
''Title:'' '''Massive Dual Gravity Revisited'''<br />
<br />
''Abstract:'' I will describe a highly speculative model of gravity as a massive,<br />
pure spin 2 field, which is "dual" to the usual description in terms of<br />
a spacetime metric tensor.<br />
<br />
In the dual description, for weak fields, the metric emerges as the<br />
field strength of an underlying fundamental field. More generally, if<br />
the gravitational field is not weak, the metric emerges as a nonlinear<br />
mixture involving the energy momentum tensor.<br />
<br />
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<br />
=== Wednesday, October 9th, 2019, 4 - 5 pm in Keck 370, refreshments from 3:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Alain Hénaut, Institut de Mathématiques de Bordeaux, Université de Bordeaux, France''' ====<br />
<br />
''Title:'' '''On planar web geometry'''<br />
<br />
''Abstract:'' Web geometry deals with foliations in general position. In the planar case and the complex setting, a $d$-web is given by the generic family of integral curves of an analytic or an algebraic differential equation $F(x,y,y')=0$ with $y'$-degree $d$. Invariants of these configurations as abelian relations (related to Abel's addition theorem), Lie symmetries or Godbillon-Vey sequences are investigated. This viewpoint enlarges the qualitative study of differential equations and their moduli. In the nonsingular case and through the singularities, Cartan-Spencer and meromorphic connections methods will be used. Basic examples will be given from different domains including classic algebraic geometry and WDVV-equations. Standard results and open problems will be mentioned. Illustration of the interplay between differential and algebraic geometry, new results will be presented. <br />
<br />
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<br />
=== Thursday, September 5th, 2019, 4 - 5 pm in Keck 171, refreshments from 3:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Nicole Yunger Halpern, Harvard-Smithsonian ITAMP (Institute for Theoretical Atomic, Molecular, and Optical Physics) Harvard University Department of Physics''' ====<br />
<br />
''Title:'' '''Entropic uncertainty relations for quantum-information scrambling'''<br />
<br />
''Abstract:'' How violently do two quantum operators disagree? Different subfields of physics feature different notions of incompatibility: (i) In quantum information theory, uncertainty relations are cast in terms of entropies. These entropic uncertainty relations constrain measurement outcomes. (ii) Condensed matter and high-energy physics feature interacting quantum many-body systems, such as spin chains. A local perturbation, such as a Pauli operator on one side of a chain, spreads through many-body entanglement. The perturbation comes to overlap, and to disagree, with probes localized on the opposite side of the system. This disagreement signals that quantum information about the perturbation has scrambled, or become hidden in highly nonlocal correlations. I will unite these two notions of quantum operator disagreement, presenting an entropic uncertainty relation for quantum-information scrambling. The entropies are of distributions over weak and strong measurements’ possible outcomes. The uncertainty bound strengthens when a spin chain scrambles in numerical simulations. Hence the subfields—quantum information, condensed matter, and high-energy physics—can agree about when quantum operations disagree. Our relation can be tested experimentally with superconducting qubits, trapped ions, and quantum dots.<br />
<br />
NYH, Bartolotta, and Pollack, Comms. Phys. 2, 92 (2019). https://www.nature.com/articles/s42005-019-0179-8<br />
<br />
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<br />
=== Monday, August 26, 2019, 7 - 8:30 pm, in Argyros Forum, Room 209 A&B, networking from 6:15 to 7pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Frederick Eberhardt, Professor of Philosophy in the Division of the Humanities and Social Sciences at the California Institute of Technology''' ====<br />
<br />
''Title:'' '''Computing Causal Relations at Scale or Causality: From Aristotle through Computing to Zebrafish'''<br />
<br />
''Abstract:'' What causes what? How do we untangle the “why” behind processes that regulate the brain, the climate or the economy? If “Correlation does not imply causation" is the standard mantra in science, how can we ever discover causal relationships behind the data? Will it ever be possible for intelligent AI to make its own deductions and predictions? In recent years researchers have developed mathematical techniques that give us the power to infer the underlying “why” behind scientific data. What’s more, we’ve learned that we can discover these causes without performing experiments. Starting with a little practical example with lightbulbs that can be worked out by hand we will see how the problem scales as the number of variables increases. To compute the neural connections in a zebrafish brain, high performance computing is essential.<br />
<br />
''Bio:'' Frederick Eberhardt is Professor of Philosophy in the Division of the Humanities and Social Sciences at the California Institute of Technology. Before coming to Caltech he was Assistant Professor in the Philosophy-Neuroscience-Psychology (PNP) program and the Department of Philosophy at Washington University in St. Louis and a postdoc at the Institute of Cognitive and Brain Sciences at the University of California, Berkeley. As an undergraduate he attended the London School of Economics for a Bachelor in Philosophy & Mathematics. He received his PhD in philosophy from Carnegie Mellon University, where he also completed a Masters in Machine Learning.<br />
<br />
His research interests lie at the intersection of philosophy of science, machine learning and statistics. He is particularly interested in the development of methods for causal discovery from statistical data.<br />
<br />
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<br />
<br />
== Spring 2019 ==<br />
<br />
The seminar talks are held in '''Keck Center for Science and Engineering, KC 171''' (Center St. Orange, CA 92866, intersection of Center St. And Sycamore St.), '''usually on Wednesday at 4 pm'''.<br />
Sometimes there will be a change of time or venue and the announcement will reflect this change.<br />
<br />
See [http://www.chapman.edu/about/maps-directions/index.aspx Maps<br />
and directions], Keck Center is Building 28 on the Campus Map [https://www.chapman.edu/about/_files/maps-and-directions/current-maps/campus-map.pdf <br />
Campus map]<br />
<br />
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<br />
=== Thursday, May 16, 2019 at 3 pm, in Keck 370, tea and cookies at 2:40pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Dr. Purbita Jana, The Institute of Mathematical Sciences, Chennai, India''' ====<br />
<br />
''Title:'' '''Intuitionistic topological systems and their connections with Heyting algebra and Gödel algebra'''<br />
<br />
''Abstract:'' (joint work with Antonio Di Nola and Revaz Grigolia) This talk will suggest a new approach of representation of a Heyting algebra as an I-topological system. I-topological systems will be introduced following the notion of topological system introduced by S. Vickers which is a triple (X, |=, A) consisting of a non-empty set X, a frame A and a relation between X and A satisfying logic of finite observations or geometric logic. It is well known that frame is the Lindenbaum algebra of geometric logic where as the Lindenbaum algebra of intuitionistic logic is a Heyting algebra. Hence to define I-topological systems, intuitionistic logic plays a crucial role. Moreover, we will focus on the categorical relationships between the I-topological system, Esakia space and Heyting algebra (and its particular case of Gödel algebra).<br />
<br />
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<br />
=== Tuesday, April 16, 2019 at 5 pm, in Keck 370, tea and cookies at 3:40pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Dr. Michele Piazzai, University of Amsterdam, Netherlands''' ====<br />
<br />
''Title:'' '''The Ecology of Ideas: Computational Evidence of Self-Organization'''<br />
<br />
''Abstract:'' Concepts are cognitive structures that people use to categorize objects and organize their knowledge of the world. Common examples include food and furniture, but also rock'n'roll, quantum physics, and blockchain. For individuals, concepts are the main tools of learning and inference; for groups of individuals (i.e., social systems), they are indispensable instruments of coordination and exchange. But how can the idiosyncratic knowledge of individuals in a social system converge on shared concepts, so as to allow coordination? Conventional wisdom in social science suggests that designated mediators, such as music critics, facilitate this convergence by endorsing the learning and usage of particular concepts. By contrast, I will argue that rational decisions embedded in everyday social interaction provide the necessary and sufficient conditions for concepts' convergence. No mediators are needed for the agents to develop a shared conceptual structure: as commonly occurs in complex adaptive systems, design emerges in the absence of centralized designers. Simulation results are presented that illustrate this point.<br />
<br />
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<br />
=== Thursday, April 11, 2019 at 4 pm, in Keck 370, tea and cookies at 3:40pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Dr. Michele Piazzai, University of Amsterdam, Netherlands''' ====<br />
<br />
''Title:'' '''The Ecology of Ideas: Empirical Evidence of Evolutionary Pressure'''<br />
<br />
''Abstract:'' Building on the notion that the collective cognition of agents engaged in social interaction constitutes a complex adaptive system, I present a theoretical framework to describe agents' shared conceptual structure as a self-replicating network of objects, ideas, and decisions. Finite cognitive resources at the agents' disposal create a competitive environment where concepts vie to be assigned to objects in categorization decisions, so as to survive in the agents' memory. This struggle for survival gives the socio-cognitive system traits characteristic of an ecology. I identify two sources of ecological interdependence among concepts, including horizontal relations between concepts located at the same level of abstraction and vertical relations between concepts located at different levels. An empirical model is developed to test whether these relations affect the selection of concepts in agents' decisions and the evolution of their shared conceptual structure. To test this model, I analyze one decade's worth of categorization decisions made by users of a crowd-sourced music encyclopedia whose objective is sorting records into genres and sub-genres.<br />
<br />
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<br />
=== Thursday, March 28, 2019 at 5 pm, in Keck 171, tea and cookies at 4:40pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Prof. Giovanni Sambin, University of Padova, Italy''' ====<br />
<br />
''Title:'' '''Half way to Grothendieck's aim (embedding of pointwise topology into pointfree topology)'''<br />
<br />
''Abstract:'' For a mathematician, the most interesting motivation for a different foundation is when it offers a new perspective or even a solution to an old problem. Developing topology over a very "weak" foundation offers a precise mathematical expression and proof to the expectation, which is well present since the time of Grothendieck, of a notion of space generalising that of topological space.<br />
The well-known link between pointfree and standard topology (with points) is a categorical adjunction between topological spaces Top and locales Loc. Using a "weak" foundation to develop topology, one is compelled to preserve more information than usual, and thus replace topological spaces with "concrete spaces", and locales with "positive topologies". Contrary to a common expectation, it is precisely this "useless" information what offers a solution to Grothendieck's aim. That is, the above adjunction becomes a categorical embedding of concrete spaces into positive topologies.<br />
This embedding does not look possible without exploiting the presence of the new (intrinsically existential) notion of positivity relation.<br />
Half way because this leaves the problem open of finding a suitable notion of positivity (formal closed subsets) in the framework of arbitrary Grothendieck topologies.<br />
<br />
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<br />
=== Wednesday, March 13, 2019 at 4 pm, in Keck 171, tea and cookies at 3:45pm in Keck 370 ===<br />
<br />
==== ''Speaker:'' '''Dr. Matt Pusey, University of Oxford''' ====<br />
<br />
''Title:'' '''Anomalous weak values and contextuality: robustness and imaginary<br />
parts'''<br />
<br />
''Abstract:'' I will discuss extensions to my previous work linking anomalous weak<br />
values with contextuality. In particular, I will show that using<br />
transformation noncontextuality obviates the experimentally<br />
problematic requirement that the post-selection is projective. I will<br />
also discuss the status of the imaginary part of weak values. My talk<br />
will be based on joint work with Ravi Kunjwal and Matteo Lostaglio:<br />
https://arxiv.org/abs/1812.06940<br />
<br />
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<br />
=== Wednesday, February 27, 2019 at 4 pm, in Keck 171, tea and cookies at 3:45pm in Keck 370 ===<br />
<br />
==== ''Speaker:'' '''Prof. Christos Tzounis, California State Polytechnic University, Pomona''' ====<br />
<br />
''Title:'' '''Metric of an Evaporating Black Hole'''<br />
<br />
''Abstract:'' We present an approximate time-dependent metric in ingoing Eddington-Finkelstein coordinates for an evaporating nonrotating black hole as a first-order perturbation of the Schwarzschild metric, using the linearized back reaction from a realistic approximation to the stress-energy tensor for the Hawking radiation in the Unruh quantum state.<br />
<br />
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<br />
=== Wednesday, February 13, 2019 at 4 pm, in Keck 171, tea and cookies at 3:45pm in Keck 370 ===<br />
<br />
==== ''Speaker:'' '''Prof. Peter Rakitzis, Institute of Electronic Structure and Laser, Heraklion, Greece''' ====<br />
<br />
''Title:'' '''Ultrahigh-Density Spin-Polarized H and D Atoms Observed via Magnetization Quantum Beats'''<br />
<br />
''Abstract:'' We measure nuclear and electron spin-polarized H and D densities of at least $10^{20}$ cm$^{−3}$ and $10^{19}$ cm$^{−3}$, i.e., at pressures of 5 bar and 0.5 bar, respectively, with ∼10-50 ns lifetimes, from the photodissociation of HBr and DI with circularly polarized UV light pulses. We observe the hyperfine quantum beating of the H and D magnetization with a pickup coil, i.e., the respective 0.7 and 3 ns periodic transfer of polarization from the electrons to the nuclei and back. These pulsed densities are ∼7 orders of magnitude higher than that produced by conventional continuous-production methods, and are sufficient for three novel applications: (a) laser-driven ion acceleration of spin-polarized electrons, protons, or deuterons, (b) the preparation of nuclear-spin-polarized molecules, and (c) the demonstration of spin-polarized D-T or D$^{-3}$He laser fusion at large laser facilities such as NIF, for which a reactivity enhancement of ∼50% is expected.<br />
<br />
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<br />
=== Tuesday, February 5 -- Saturday, February 9, 2019 in Keck 370 ===<br />
<br />
==== '''11th Annual Chapman University CECAT Workshop on Pointfree Mathematics''' ====<br />
<br />
TUESDAY, February 5th:<br />
<br />
1:00 - 2:00pm '''M. Andrew Moshier''', ''Chapman University'', Weakening relations<br />
<br />
THURSDAY, February 7th:<br />
<br />
10:30 - 11:30am: '''Peter Jipsen''', ''Chapman University'', Involutive residuated lattices and relation algebras<br />
<br />
11:30 - 12:30pm: '''Sara Vannucci''', ''University of Salerno'', Semiring and Semimodule Issues in Residuated Lattices<br />
<br />
1:00 - 2:15pm: '''Rick Ball''', ''University of Denver'', Pointfree Integration<br />
<br />
2:15 - 3:15pm: '''Anna Laura Suarez''', ''University of Birmingham'', D-frames and frame coproducts<br />
<br />
3:30 - 4.30pm: '''Alex Kurz''', ''Chapman University'', On the duality theory of weakening relations<br />
<br />
FRIDAY, February 8th<br />
<br />
10:30 - 11:30am: '''Ales Pultr''', ''Charles University'', Strong Hausdorff properties of frames<br />
<br />
11:30 - 12:30pm: '''Diego Valota''', ''University of Milan'', [http://math.chapman.edu/~jipsen/cecat/11th-Pointfree-Mathematics-Workshop/DiegoValota2019.pdf Computing Spectra via Dualities in the MTL hierarchy]<br />
<br />
2:00 - 3:00pm: '''Olim Tuyt''', ''University of Bern'', Algebraic finite model property of a modal Gödel logic<br />
<br />
3:00 - 4:15pm: '''Rick Ball''', ''University of Denver'', Pointfree Integration, continued<br />
<br />
SATURDAY, February 9th<br />
<br />
1:00 - 5:00pm: Discussion session<br />
<br />
<br />
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----</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=MPC_Seminar&diff=28MPC Seminar2021-09-17T20:36:48Z<p>Jipsen: /* Wednesday, September 22, 2021, 4 - 5 pm in KC 370 */</p>
<hr />
<div>This is the homepage of the Chapman University '''Mathematics, Physics, and Computation Seminars'''<br />
([[MPC Seminar]])<br />
<br />
''Seminar Organizers:'' Roman Buniy and Peter Jipsen<br />
<br />
<br />
== Fall 2021 ==<br />
<br />
The MPC seminar is held in-person in the '''Keck Center of Science and Engineering, Room 370''' (unless a speaker prefers to hold the talk over Zoom). The date and time are included in the announcements below.<br />
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=== Thursday, September 23, 2021, 12:30 - 1:30 pm in AF 209C ===<br />
<br />
==== ''Speaker:'' '''Lev Vaidman''' ====<br />
<br />
''Title:'' '''Counterfactual communication'''<br />
<br />
''Abstract:'' Possibility to communicate between spatially separated regions, without even a single photon passing between the two parties, is an amazing quantum phenomenon. The possibility of transmitting one value of a bit in such a way, the interaction-free measurement, was known for a quarter of a century. The protocols of full communication, including transmitting unknown quantum states were proposed only a few years ago, but it was shown that in all these protocols the particle was leaving a weak trace in the transmission channel, the trace larger than the trace left by a single particle passing through the channel. However, a simple modification of these recent protocols eliminates the trace in the transmission channel and makes all these protocols truly counterfactual.<br />
<br />
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<br />
== Spring 2021 ==<br />
<br />
<br />
=== Monday, May 3rd, 2021, 1 - 2 pm on Zoom ===<br />
<br />
==== ''Speaker:'' '''Simon Henry, University of Ottawa''' ====<br />
<br />
''Title:'' '''Localic C*-algebras and the Geometric Bohr topos'''<br />
<br />
''Abstract:'' The Bohr topos is a space attached to a C*-algebra A that has been introduced in the hope of producing a new point of view on the mathematics of Quantum mechanics. It is essentially the "space of commutative sub-C*-algebra of A". But its original construction had two problems: (1) it had "the wrong topology" and (2) it was a "non-geometric" construction, i.e. when applied to continuous families of C*-algebras, it wasn't compatible with certain change-of-base functors. In this talk I'll explain how the theory of localic C*-algebras and some classical idea from "geometric logic" allows to give a new version of this construction that solves both of these problems.<br />
<br />
''Link to paper:'' [https://arxiv.org/pdf/1502.01896.pdf arxiv.org/pdf/1502.01896.pdf]<br />
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<br />
<br />
=== Thursday, Jan 21st, 2021, 4 - 5 pm on Zoom ===<br />
<br />
==== ''Speaker:'' '''Mike Campbell, Eureka (SAP), joint work with Vernon Smith (Chapman University)''' ====<br />
<br />
''Title:'' '''An Elementary Humanomics Approach to Boundedly Rational Quadratic Models'''<br />
<br />
''Video of talk:'' [https://youtu.be/F74RlCAjC_A YouTube] ''Slides:'' [http://math.chapman.edu/~jipsen/seminarposters/MikeCampbell2021HumanomicsApproachBRQuadratic.pdf pdf]<br />
<br />
''Abstract:'' We take a refreshing new look at boundedly rational quadratic models in economics using some elementary modeling of the principles put forward in the book Humanomics by Vernon L. Smith and Bart J. Wilson. A simple model is introduced built on the fundamental Humanomics principles of gratitude/resentment felt and the corresponding action responses of reward/punishment in the form of higher/lower payoff transfers. There are two timescales: one for strictly self-interested action, as in economic equilibrium, and another governed by feelings of gratitude/resentment. One of three timescale scenarios is investigated: one where gratitude/resentment changes much more slowly than economic equilibrium ("quenched model"). Another model, in which economic equilibrium occurs over a much slower time than gratitude/resent evolution ("annealed model") is set up, but not investigated. The quenched model with homogeneous interactions turns out to be a non-frustrated spin-glass model. A two-agent quenched model with heterogeneous aligning (ferromagnetic) interactions is analyzed and yields new insights into the critical quenched probability p (1-p) that represents the empirical frequency of opportunity for agent i to take action for the benefit (hurt) of other that invokes mutual gratitude (resentment). A critical quenched probability p*i, i=1,2, exists for each agent. When p < p*i, agent i will choose action in their self-interest. When p > p*i, agent i will take action sensitive to their interpersonal feelings of gratitude/resentment and thus reward/punish the initiating benefit/hurt. We find that the p*i are greater than one-half, which implies agents are averse to resentful behavior and punishment. This was not built into the model, but is a result of its properties, and consistent with Axiom 4 in Humanomics about the asymmetry of gratitude and resentment. Furthermore, the agent who receives less payoff is more averse to resentful behavior; i.e., has a higher critical quenched probability. For this particular model, the Nash equilibrium has no predictive power of Humanomics properties since the rewards are the same for self-interested behavior, resentful behavior, and gratitude behavior. Accordingly, we see that the boundedly rational Gibbs equilibrium does indeed lead to richer properties.<br />
<br />
''Link to paper:'' [https://digitalcommons.chapman.edu/cgi/viewcontent.cgi?article=1330&context=esi_working_papers Chapman Digital Commons]<br />
<br />
== Spring 2020 ==<br />
<br />
The seminar talks are held in '''Keck Center for Science and Engineering, KC 370''' (Center St. Orange, CA 92866, intersection of Center St. And Sycamore St.), '''usually on Wednesday at 4 pm'''.<br />
Sometimes there will be a change of time or venue and the announcement will reflect this change.<br />
<br />
See [http://www.chapman.edu/about/maps-directions/index.aspx Maps<br />
and directions], Keck Center is Building 28 on the Campus Map [https://www.chapman.edu/about/_files/maps-and-directions/current-maps/campus-map.pdf <br />
Campus map]<br />
<br />
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<br />
<br />
=== Friday, Feb 21st, 2020, noon - 1 pm in Keck 370, refreshments at 11:45 am (same room) ===<br />
<br />
==== ''Speaker:'' '''Christian Williams, University of California at Riverside''' ====<br />
<br />
''Title:'' '''Predicate Calculus for Algebraic Theories'''<br />
<br />
''Abstract:'' There is a notion of predicate for algebraic theories, which admits a calculus of both logical and algebraic operations. We thereby extend equational logic by first-order logic, and provide a natural type theory for algebraic structures.<br />
<br />
We demonstrate the idea with the theory of monoids, and derive the example predicate "prime". This and many algebraic examples are only useful when they are mapped from a theory into actual models. There is much to be done in this direction. However, the driving motivation of this work is the application to programming languages: we focus on applying the idea to a more general notion of theory with variable binding.<br />
<br />
The construction is given in the topos of presheaves on a theory T: a "predicate" is a sieve on an object t of T, which corresponds to a subfunctor of the representable T(-,t). For each type t, these predicates form a Heyting algebra, providing the constructors of intuitionistic logic. The operations of T can be lifted to act on predicates, and we construct a model Pred(T): T -->HeyAlg. The correspondence between the operations of T and those in the image of Pred(T) gives that the former are "polymorphic" with respect to the types of the latter. This process can be understood as providing the theory T with a polymorphic type system.<br />
<br />
The original motivation of this work is a logic for concurrency known as Namespace Logic. This applies to the reflective higher-order pi calculus, which is the language of the distributed computing platform RChain. We demonstrate the above framework by constructing namespace logic. This gives a glimpse into a large field of potential application.<br />
<br />
[http://math.chapman.edu/~jipsen/seminarposters/Christian_Williams_pcat_2020-02-21.pdf Slides from the talk]<br />
<br />
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=== Wednesday, Feb 19th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Simon Cho, University of Michigan''' ====<br />
''Title:'' '''A categorical perspective on persistent and magnitude homology'''<br />
<br />
''Abstract:'' We define and explain both persistent homology and magnitude homology, and their respective roles in applications (in both pure and applied settings). We will exhibit how both arise as a "singular complex" of a metric space in essentially the same way, but for different values of a parameter.<br />
<br />
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<br />
=== Wednesday, Feb 12th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Stephon Alexander, Brown University, Rhode Island''' ====<br />
''Title:'' '''The Quantum Cosmological Constant'''<br />
<br />
''Abstract:'' The mysteries surrounding the Cosmological Constant presides at the interface of quantum mechanics and gravity. In this seminar,<br />
I will provide a pedagogical discussion of the many faces of the cosmological constant problem and discuss some current research that<br />
paves new directions that invites us to rethink the quantum nature of vacuum energy.<br />
<br />
<br />
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<br />
=== Tuesday, Jan 14th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Pedram Roushan, Google Inc., Santa Barbara, CA''' ====<br />
''Title:'' '''Quantum supremacy using a programmable superconducting processor'''<br />
<br />
''Abstract:'' The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor1. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 2^53 (about 10^16). Measurements from repeated experiments sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 seconds to sample one instance of a quantum circuit a million times—our benchmarks currently indicate that the equivalent task for a state-of-the-art classical supercomputer would take approximately 10,000 years. This dramatic increase in speed compared to all known classical algorithms is an experimental realization of quantum supremacy for this specific computational task, heralding a much-anticipated computing paradigm. If time permits, I will present some of our more recent measurements. <br />
<br />
<br />
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----<br />
<br />
== Fall 2019 ==<br />
<br />
The seminar talks are held in '''Keck Center for Science and Engineering, KC 370''' (Center St. Orange, CA 92866, intersection of Center St. And Sycamore St.), '''usually on Wednesday at 4 pm'''.<br />
Sometimes there will be a change of time or venue and the announcement will reflect this change.<br />
<br />
See [http://www.chapman.edu/about/maps-directions/index.aspx Maps<br />
and directions], Keck Center is Building 28 on the Campus Map [https://www.chapman.edu/about/_files/maps-and-directions/current-maps/campus-map.pdf <br />
Campus map]<br />
<br />
<br />
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----<br />
<br />
=== Thursday, Dec 12th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Alí Guzmán Adán, Universiteit Gent, Belgium''' ====<br />
''Title:'' '''Pizzetti and Cauchy formulae for higher dimensional surfaces: a<br />
distributional approach'''<br />
<br />
''Abstract:'' In this talk, we study Pizzetti-type formulas for Stiefel<br />
manifolds and Cauchy-type formulas for the tangential Dirac operator<br />
from a distributional perspective. First, we illustrate a general<br />
distributional method for integration over manifolds in R^m defined by<br />
means of k equations. We apply this method to derive an alternative<br />
proof of the Pizzetti formulae for the real Stiefel manifolds<br />
SO(m)/SO(m-k). Besides, a distributional interpretation of invariant<br />
oriented integration is provided. In particular, we obtain a<br />
distributional Cauchy theorem for the tangential Dirac operator on an<br />
embedded (m-k)-dimensional smooth surface.<br />
<br />
<br />
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<br />
=== Wednesday, Dec 11th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Arjendu K Pattanayak, Physics and Astronomy, Carleton College, Northfield, Minnesota''' ====<br />
''Title:'' '''Quantum entanglement and tunneling oscillations in a (few) many-body nonlinear spin system'''<br />
<br />
''Abstract:'' Quantum tunnelling permits recoherence or refocusing in real or phase space after the initial quantum state has seemingly delocalized, exhibiting so-called classically forbidden dynamics. For a nonlinearly interacting many-body spin system this interim state can be an entangled state. We report on recent results from investigations into this phenomenon for initially spin coherent pure states in the paradigmatic kicked top (vale Haake) system. This has a mixed regualar and chaotic phase space in the classical limit and exhibits the entanglement tunneling described above, including coherent dynamics between phase-space stability islands; here the interim state is maximally entangled. We map the dependence on various parameters including nonlinear spin and number of spins involved (focusing mostly on the remarkable special case N=4) using a metric that attempts to quantify the quality and rate of tunnelling. The calculations of tunneling rates using eigenvalues and eigenstates of the time evolution operator as a function of initial condition compared to classical space structures demonstrates several nontrivial ways in which quantum behavior transitions to classical as the size of the system grows.<br />
<br />
<br />
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<br />
=== Wednesday, Dec 4th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Raphael Drumond, Universidade Federal de Minas Gerais, Brazil''' ====<br />
''Title:'' '''The basics of Quantum Darwinism (and its relationship with non-Markovianity)'''<br />
<br />
''Abstract:'' Some aspects of physical systems described by quantum <br />
mechanics, most notably the possibility of violating a Bell inequality, <br />
suggests (to some) or unavoidably implies (to others) that certain <br />
properties of microscopic systems, like the precise values of position <br />
and momentum of a fundamental particle, do not have an objective <br />
reality. This strongly contrasts with the objectivity of properties of <br />
everyday macroscopic systems like the (rough estimate of) position and <br />
momentum of a baseball. Now, how can this objectivity of the <br />
macroscopic world emerge from a theory where, apparently, not all <br />
aspects of physical systems are objective? The notion of quantum <br />
Darwinism, put forward and popularized by Wojciech Zurek, is a path in <br />
that direction. In this talk I will discuss the main ideas behind <br />
quantum Darwinism, explore it in some simple models, and briefly discuss <br />
its relationship (or the lack of it) with the notion of non-Markovianity <br />
of quantum dynamical systems.<br />
<br />
<br />
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----<br />
<br />
=== Thursday, Nov 21th, 2019, 12:30 - 1:30 pm in Keck 370, refreshments from 12:15 (same room) ===<br />
<br />
==== ''Speaker:'' '''Sandu Popescu, University of Bristol, UK''' ====<br />
''Title:'' '''Exploring the limits of no-backward-in-time signaling'''<br />
<br />
''Abstract:'' One of the most routine observations that we make about our world is that we cannot signal backwards in time. So ubiquitous is this understanding that it is often taken as one of the basic laws of Nature. At first glance, this remark seems straightforward. However, as I will show, in probabilistic theories such as quantum mechanics, the consequences of such an assertion are far more involved. In fact, we will see that there is a surprising amount of liberty: some theories even allow the future to affect the past, nevertheless without signaling backwards in time.<br />
<br />
<br />
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<br />
=== Friday, Nov 8th, 2019, 3 - 4 pm in Keck 171, refreshments from 2:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Fredrik Dahlqvist, University College London, UK''' ====<br />
<br />
''Title:'' '''A probabilistic approach to floating point arithmetic'''<br />
<br />
''Abstract:'' Finite-precision floating point arithmetic introduces rounding errors which are traditionally bounded using a worst-case analysis. However, worst-case analysis might be overly conservative because worst-case errors can be extremely rare events in practice. Here we develop a probabilistic model of rounding errors with which it becomes possible to quantify the likelihood that the rounding error of an algorithm lies within a given interval. <br />
<br />
Given an input distribution, the model requires the distribution of rounding errors. We show how to exactly compute this distribution for low precision arithmetic. For high precision arithmetic we derive a simple but surprisingly useful approximation. The model is then entirely compositional: given a numerical program written in a simple imperative programing language we can recursively compute the distribution of rounding errors at each step and propagate it through each program instruction. This is done by applying a formalism originaly developed by Kozen to understand the semantics of probabilistic programs, for example how probability distributions gets transformed by assignments or "if then else" statements.<br />
<br />
<br />
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<br />
=== Wednesday, Nov 6th, 2019, 4 - 5 pm in Keck 370, refreshments from 3:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Jacques Pienaar, International Institute of Physics in Natal, Brazil''' ====<br />
<br />
''Title:'' '''The new question in quantum foundations: what is causality?'''<br />
<br />
''Abstract:'' Work in quantum foundations has tended to concentrate on Bell's Theorem, <br />
but recently a particular aspect of that theorem has taken on a life of <br />
its own: the question of what "causality" means in quantum mechanics, <br />
and how to model it. This movement has been driven in large part by <br />
recent advances in causal modeling in the statistical and Artificial <br />
Intelligence communities, which have had a heavy influence on quantum <br />
causal modeling. These "classical" approaches tend to define causality <br />
as a probabilistic and action-centered concept, which fits well with <br />
modern information-theoretic treatments of quantum mechanics. However, <br />
the classical approaches also tend to emphasize notions of underlying <br />
determinism and objective mechanisms that do not sit so well in the <br />
quantum context. In this talk I will step back from most of the <br />
technical jargon and try to get to the heart of some of the conceptual <br />
issues involved in "quantizing" the concept of causality, critically <br />
reviewing some key findings, pointing out potential inconsistencies and <br />
outlining possible directions for further inquiry into this fascinating <br />
problem.<br />
<br />
<br />
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----<br />
<br />
=== Friday, October 18th, 2019, 12 - 1 pm in Keck 370, refreshments from 11:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Prof. Lev Vaidman, Alex Maguy-Glass Chair in Physics of Complex Systems, Tel Aviv University, Israel''' ====<br />
<br />
''Title:'' '''The past of a quantum particle'''<br />
<br />
''Abstract:'' Textbooks of quantum mechanics lack the concept of the past of quantum systems. Few years ago I proposed to define the past of a quantum particle according to the trace it leaves. While in many cases this definition provides a reasonable description, for a nested Mach-Zehnder interferometer it leads to a picture seemingly contradicting common sense: the particle leaves a trace in a place through which it could not pass. I will discuss recent theoretical and experimental studies of this controversial issue.<br />
<br />
<br />
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----<br />
<br />
=== Friday, October 11th, 2019, 1 - 2 pm in Keck 370, refreshments from 12:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Prof. Thomas Curtright, University of Miami''' ====<br />
<br />
''Title:'' '''Massive Dual Gravity Revisited'''<br />
<br />
''Abstract:'' I will describe a highly speculative model of gravity as a massive,<br />
pure spin 2 field, which is "dual" to the usual description in terms of<br />
a spacetime metric tensor.<br />
<br />
In the dual description, for weak fields, the metric emerges as the<br />
field strength of an underlying fundamental field. More generally, if<br />
the gravitational field is not weak, the metric emerges as a nonlinear<br />
mixture involving the energy momentum tensor.<br />
<br />
<br />
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----<br />
<br />
=== Wednesday, October 9th, 2019, 4 - 5 pm in Keck 370, refreshments from 3:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Alain Hénaut, Institut de Mathématiques de Bordeaux, Université de Bordeaux, France''' ====<br />
<br />
''Title:'' '''On planar web geometry'''<br />
<br />
''Abstract:'' Web geometry deals with foliations in general position. In the planar case and the complex setting, a $d$-web is given by the generic family of integral curves of an analytic or an algebraic differential equation $F(x,y,y')=0$ with $y'$-degree $d$. Invariants of these configurations as abelian relations (related to Abel's addition theorem), Lie symmetries or Godbillon-Vey sequences are investigated. This viewpoint enlarges the qualitative study of differential equations and their moduli. In the nonsingular case and through the singularities, Cartan-Spencer and meromorphic connections methods will be used. Basic examples will be given from different domains including classic algebraic geometry and WDVV-equations. Standard results and open problems will be mentioned. Illustration of the interplay between differential and algebraic geometry, new results will be presented. <br />
<br />
<br />
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----<br />
<br />
=== Thursday, September 5th, 2019, 4 - 5 pm in Keck 171, refreshments from 3:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Nicole Yunger Halpern, Harvard-Smithsonian ITAMP (Institute for Theoretical Atomic, Molecular, and Optical Physics) Harvard University Department of Physics''' ====<br />
<br />
''Title:'' '''Entropic uncertainty relations for quantum-information scrambling'''<br />
<br />
''Abstract:'' How violently do two quantum operators disagree? Different subfields of physics feature different notions of incompatibility: (i) In quantum information theory, uncertainty relations are cast in terms of entropies. These entropic uncertainty relations constrain measurement outcomes. (ii) Condensed matter and high-energy physics feature interacting quantum many-body systems, such as spin chains. A local perturbation, such as a Pauli operator on one side of a chain, spreads through many-body entanglement. The perturbation comes to overlap, and to disagree, with probes localized on the opposite side of the system. This disagreement signals that quantum information about the perturbation has scrambled, or become hidden in highly nonlocal correlations. I will unite these two notions of quantum operator disagreement, presenting an entropic uncertainty relation for quantum-information scrambling. The entropies are of distributions over weak and strong measurements’ possible outcomes. The uncertainty bound strengthens when a spin chain scrambles in numerical simulations. Hence the subfields—quantum information, condensed matter, and high-energy physics—can agree about when quantum operations disagree. Our relation can be tested experimentally with superconducting qubits, trapped ions, and quantum dots.<br />
<br />
NYH, Bartolotta, and Pollack, Comms. Phys. 2, 92 (2019). https://www.nature.com/articles/s42005-019-0179-8<br />
<br />
<br />
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<br />
=== Monday, August 26, 2019, 7 - 8:30 pm, in Argyros Forum, Room 209 A&B, networking from 6:15 to 7pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Frederick Eberhardt, Professor of Philosophy in the Division of the Humanities and Social Sciences at the California Institute of Technology''' ====<br />
<br />
''Title:'' '''Computing Causal Relations at Scale or Causality: From Aristotle through Computing to Zebrafish'''<br />
<br />
''Abstract:'' What causes what? How do we untangle the “why” behind processes that regulate the brain, the climate or the economy? If “Correlation does not imply causation" is the standard mantra in science, how can we ever discover causal relationships behind the data? Will it ever be possible for intelligent AI to make its own deductions and predictions? In recent years researchers have developed mathematical techniques that give us the power to infer the underlying “why” behind scientific data. What’s more, we’ve learned that we can discover these causes without performing experiments. Starting with a little practical example with lightbulbs that can be worked out by hand we will see how the problem scales as the number of variables increases. To compute the neural connections in a zebrafish brain, high performance computing is essential.<br />
<br />
''Bio:'' Frederick Eberhardt is Professor of Philosophy in the Division of the Humanities and Social Sciences at the California Institute of Technology. Before coming to Caltech he was Assistant Professor in the Philosophy-Neuroscience-Psychology (PNP) program and the Department of Philosophy at Washington University in St. Louis and a postdoc at the Institute of Cognitive and Brain Sciences at the University of California, Berkeley. As an undergraduate he attended the London School of Economics for a Bachelor in Philosophy & Mathematics. He received his PhD in philosophy from Carnegie Mellon University, where he also completed a Masters in Machine Learning.<br />
<br />
His research interests lie at the intersection of philosophy of science, machine learning and statistics. He is particularly interested in the development of methods for causal discovery from statistical data.<br />
<br />
<br />
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<br />
<br />
<br />
== Previous Seminar talks ==<br />
<br />
* [[MPC Seminar 2019]]<br />
<br />
* [[MPC Seminar 2018]]<br />
<br />
* [[MathCS Seminar 2017]]<br />
<br />
* [[MathCS Seminar 2016]]<br />
<br />
* [[MathCS Seminar 2015]]<br />
<br />
* [[MathCS Seminar 2014]]<br />
<br />
* [[MathCS Seminar 2013]]<br />
<br />
* [[MathCS Seminar 2012]]<br />
<br />
* [[MathCS Seminar 2011]]<br />
<br />
* [[MathCS Seminar 2010]]<br />
<br />
* [[MathCS Seminar 2009]]<br />
<br />
* [[MathCS Seminar 2008]]<br />
<br />
* [[MathCS Seminar 2007]]<br />
<br />
* [[MathCS Seminar 2006]]<br />
<br />
* [[MathCS Seminar 2005]]<br />
<br />
* [[MathCS Seminar 2004]]<br />
<br />
* [[MathCS Seminar 2003]]<br />
<br />
* [[MathCS Seminar 2002]]</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=MPC_Seminar&diff=27MPC Seminar2021-09-15T00:49:55Z<p>Jipsen: </p>
<hr />
<div>This is the homepage of the Chapman University '''Mathematics, Physics, and Computation Seminars'''<br />
([[MPC Seminar]])<br />
<br />
''Seminar Organizers:'' Roman Buniy and Peter Jipsen<br />
<br />
<br />
== Fall 2021 ==<br />
<br />
The MPC seminar is held in-person in the '''Keck Center of Science and Engineering, Room 370''' (unless a speaker prefers to hold the talk over Zoom). The date and time are included in the announcements below.<br />
<br />
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=== Wednesday, September 22, 2021, 4 - 5 pm in KC 370 ===<br />
<br />
==== ''Speaker:'' '''Lev Vaidman''' ====<br />
<br />
''Title:'' '''Counterfactual communication'''<br />
<br />
''Abstract:'' Possibility to communicate between spatially separated regions, without even a single photon passing between the two parties, is an amazing quantum phenomenon. The possibility of transmitting one value of a bit in such a way, the interaction-free measurement, was known for a quarter of a century. The protocols of full communication, including transmitting unknown quantum states were proposed only a few years ago, but it was shown that in all these protocols the particle was leaving a weak trace in the transmission channel, the trace larger than the trace left by a single particle passing through the channel. However, a simple modification of these recent protocols eliminates the trace in the transmission channel and makes all these protocols truly counterfactual.<br />
<br />
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<br />
== Spring 2021 ==<br />
<br />
<br />
=== Monday, May 3rd, 2021, 1 - 2 pm on Zoom ===<br />
<br />
==== ''Speaker:'' '''Simon Henry, University of Ottawa''' ====<br />
<br />
''Title:'' '''Localic C*-algebras and the Geometric Bohr topos'''<br />
<br />
''Abstract:'' The Bohr topos is a space attached to a C*-algebra A that has been introduced in the hope of producing a new point of view on the mathematics of Quantum mechanics. It is essentially the "space of commutative sub-C*-algebra of A". But its original construction had two problems: (1) it had "the wrong topology" and (2) it was a "non-geometric" construction, i.e. when applied to continuous families of C*-algebras, it wasn't compatible with certain change-of-base functors. In this talk I'll explain how the theory of localic C*-algebras and some classical idea from "geometric logic" allows to give a new version of this construction that solves both of these problems.<br />
<br />
''Link to paper:'' [https://arxiv.org/pdf/1502.01896.pdf arxiv.org/pdf/1502.01896.pdf]<br />
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<br />
<br />
=== Thursday, Jan 21st, 2021, 4 - 5 pm on Zoom ===<br />
<br />
==== ''Speaker:'' '''Mike Campbell, Eureka (SAP), joint work with Vernon Smith (Chapman University)''' ====<br />
<br />
''Title:'' '''An Elementary Humanomics Approach to Boundedly Rational Quadratic Models'''<br />
<br />
''Video of talk:'' [https://youtu.be/F74RlCAjC_A YouTube] ''Slides:'' [http://math.chapman.edu/~jipsen/seminarposters/MikeCampbell2021HumanomicsApproachBRQuadratic.pdf pdf]<br />
<br />
''Abstract:'' We take a refreshing new look at boundedly rational quadratic models in economics using some elementary modeling of the principles put forward in the book Humanomics by Vernon L. Smith and Bart J. Wilson. A simple model is introduced built on the fundamental Humanomics principles of gratitude/resentment felt and the corresponding action responses of reward/punishment in the form of higher/lower payoff transfers. There are two timescales: one for strictly self-interested action, as in economic equilibrium, and another governed by feelings of gratitude/resentment. One of three timescale scenarios is investigated: one where gratitude/resentment changes much more slowly than economic equilibrium ("quenched model"). Another model, in which economic equilibrium occurs over a much slower time than gratitude/resent evolution ("annealed model") is set up, but not investigated. The quenched model with homogeneous interactions turns out to be a non-frustrated spin-glass model. A two-agent quenched model with heterogeneous aligning (ferromagnetic) interactions is analyzed and yields new insights into the critical quenched probability p (1-p) that represents the empirical frequency of opportunity for agent i to take action for the benefit (hurt) of other that invokes mutual gratitude (resentment). A critical quenched probability p*i, i=1,2, exists for each agent. When p < p*i, agent i will choose action in their self-interest. When p > p*i, agent i will take action sensitive to their interpersonal feelings of gratitude/resentment and thus reward/punish the initiating benefit/hurt. We find that the p*i are greater than one-half, which implies agents are averse to resentful behavior and punishment. This was not built into the model, but is a result of its properties, and consistent with Axiom 4 in Humanomics about the asymmetry of gratitude and resentment. Furthermore, the agent who receives less payoff is more averse to resentful behavior; i.e., has a higher critical quenched probability. For this particular model, the Nash equilibrium has no predictive power of Humanomics properties since the rewards are the same for self-interested behavior, resentful behavior, and gratitude behavior. Accordingly, we see that the boundedly rational Gibbs equilibrium does indeed lead to richer properties.<br />
<br />
''Link to paper:'' [https://digitalcommons.chapman.edu/cgi/viewcontent.cgi?article=1330&context=esi_working_papers Chapman Digital Commons]<br />
<br />
== Spring 2020 ==<br />
<br />
The seminar talks are held in '''Keck Center for Science and Engineering, KC 370''' (Center St. Orange, CA 92866, intersection of Center St. And Sycamore St.), '''usually on Wednesday at 4 pm'''.<br />
Sometimes there will be a change of time or venue and the announcement will reflect this change.<br />
<br />
See [http://www.chapman.edu/about/maps-directions/index.aspx Maps<br />
and directions], Keck Center is Building 28 on the Campus Map [https://www.chapman.edu/about/_files/maps-and-directions/current-maps/campus-map.pdf <br />
Campus map]<br />
<br />
<br />
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----<br />
<br />
<br />
=== Friday, Feb 21st, 2020, noon - 1 pm in Keck 370, refreshments at 11:45 am (same room) ===<br />
<br />
==== ''Speaker:'' '''Christian Williams, University of California at Riverside''' ====<br />
<br />
''Title:'' '''Predicate Calculus for Algebraic Theories'''<br />
<br />
''Abstract:'' There is a notion of predicate for algebraic theories, which admits a calculus of both logical and algebraic operations. We thereby extend equational logic by first-order logic, and provide a natural type theory for algebraic structures.<br />
<br />
We demonstrate the idea with the theory of monoids, and derive the example predicate "prime". This and many algebraic examples are only useful when they are mapped from a theory into actual models. There is much to be done in this direction. However, the driving motivation of this work is the application to programming languages: we focus on applying the idea to a more general notion of theory with variable binding.<br />
<br />
The construction is given in the topos of presheaves on a theory T: a "predicate" is a sieve on an object t of T, which corresponds to a subfunctor of the representable T(-,t). For each type t, these predicates form a Heyting algebra, providing the constructors of intuitionistic logic. The operations of T can be lifted to act on predicates, and we construct a model Pred(T): T -->HeyAlg. The correspondence between the operations of T and those in the image of Pred(T) gives that the former are "polymorphic" with respect to the types of the latter. This process can be understood as providing the theory T with a polymorphic type system.<br />
<br />
The original motivation of this work is a logic for concurrency known as Namespace Logic. This applies to the reflective higher-order pi calculus, which is the language of the distributed computing platform RChain. We demonstrate the above framework by constructing namespace logic. This gives a glimpse into a large field of potential application.<br />
<br />
[http://math.chapman.edu/~jipsen/seminarposters/Christian_Williams_pcat_2020-02-21.pdf Slides from the talk]<br />
<br />
<br />
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<br />
=== Wednesday, Feb 19th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Simon Cho, University of Michigan''' ====<br />
''Title:'' '''A categorical perspective on persistent and magnitude homology'''<br />
<br />
''Abstract:'' We define and explain both persistent homology and magnitude homology, and their respective roles in applications (in both pure and applied settings). We will exhibit how both arise as a "singular complex" of a metric space in essentially the same way, but for different values of a parameter.<br />
<br />
<br />
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<br />
=== Wednesday, Feb 12th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Stephon Alexander, Brown University, Rhode Island''' ====<br />
''Title:'' '''The Quantum Cosmological Constant'''<br />
<br />
''Abstract:'' The mysteries surrounding the Cosmological Constant presides at the interface of quantum mechanics and gravity. In this seminar,<br />
I will provide a pedagogical discussion of the many faces of the cosmological constant problem and discuss some current research that<br />
paves new directions that invites us to rethink the quantum nature of vacuum energy.<br />
<br />
<br />
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<br />
=== Tuesday, Jan 14th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Pedram Roushan, Google Inc., Santa Barbara, CA''' ====<br />
''Title:'' '''Quantum supremacy using a programmable superconducting processor'''<br />
<br />
''Abstract:'' The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor1. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 2^53 (about 10^16). Measurements from repeated experiments sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 seconds to sample one instance of a quantum circuit a million times—our benchmarks currently indicate that the equivalent task for a state-of-the-art classical supercomputer would take approximately 10,000 years. This dramatic increase in speed compared to all known classical algorithms is an experimental realization of quantum supremacy for this specific computational task, heralding a much-anticipated computing paradigm. If time permits, I will present some of our more recent measurements. <br />
<br />
<br />
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<br />
== Fall 2019 ==<br />
<br />
The seminar talks are held in '''Keck Center for Science and Engineering, KC 370''' (Center St. Orange, CA 92866, intersection of Center St. And Sycamore St.), '''usually on Wednesday at 4 pm'''.<br />
Sometimes there will be a change of time or venue and the announcement will reflect this change.<br />
<br />
See [http://www.chapman.edu/about/maps-directions/index.aspx Maps<br />
and directions], Keck Center is Building 28 on the Campus Map [https://www.chapman.edu/about/_files/maps-and-directions/current-maps/campus-map.pdf <br />
Campus map]<br />
<br />
<br />
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----<br />
<br />
=== Thursday, Dec 12th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Alí Guzmán Adán, Universiteit Gent, Belgium''' ====<br />
''Title:'' '''Pizzetti and Cauchy formulae for higher dimensional surfaces: a<br />
distributional approach'''<br />
<br />
''Abstract:'' In this talk, we study Pizzetti-type formulas for Stiefel<br />
manifolds and Cauchy-type formulas for the tangential Dirac operator<br />
from a distributional perspective. First, we illustrate a general<br />
distributional method for integration over manifolds in R^m defined by<br />
means of k equations. We apply this method to derive an alternative<br />
proof of the Pizzetti formulae for the real Stiefel manifolds<br />
SO(m)/SO(m-k). Besides, a distributional interpretation of invariant<br />
oriented integration is provided. In particular, we obtain a<br />
distributional Cauchy theorem for the tangential Dirac operator on an<br />
embedded (m-k)-dimensional smooth surface.<br />
<br />
<br />
----<br />
----<br />
<br />
=== Wednesday, Dec 11th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Arjendu K Pattanayak, Physics and Astronomy, Carleton College, Northfield, Minnesota''' ====<br />
''Title:'' '''Quantum entanglement and tunneling oscillations in a (few) many-body nonlinear spin system'''<br />
<br />
''Abstract:'' Quantum tunnelling permits recoherence or refocusing in real or phase space after the initial quantum state has seemingly delocalized, exhibiting so-called classically forbidden dynamics. For a nonlinearly interacting many-body spin system this interim state can be an entangled state. We report on recent results from investigations into this phenomenon for initially spin coherent pure states in the paradigmatic kicked top (vale Haake) system. This has a mixed regualar and chaotic phase space in the classical limit and exhibits the entanglement tunneling described above, including coherent dynamics between phase-space stability islands; here the interim state is maximally entangled. We map the dependence on various parameters including nonlinear spin and number of spins involved (focusing mostly on the remarkable special case N=4) using a metric that attempts to quantify the quality and rate of tunnelling. The calculations of tunneling rates using eigenvalues and eigenstates of the time evolution operator as a function of initial condition compared to classical space structures demonstrates several nontrivial ways in which quantum behavior transitions to classical as the size of the system grows.<br />
<br />
<br />
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----<br />
<br />
=== Wednesday, Dec 4th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Raphael Drumond, Universidade Federal de Minas Gerais, Brazil''' ====<br />
''Title:'' '''The basics of Quantum Darwinism (and its relationship with non-Markovianity)'''<br />
<br />
''Abstract:'' Some aspects of physical systems described by quantum <br />
mechanics, most notably the possibility of violating a Bell inequality, <br />
suggests (to some) or unavoidably implies (to others) that certain <br />
properties of microscopic systems, like the precise values of position <br />
and momentum of a fundamental particle, do not have an objective <br />
reality. This strongly contrasts with the objectivity of properties of <br />
everyday macroscopic systems like the (rough estimate of) position and <br />
momentum of a baseball. Now, how can this objectivity of the <br />
macroscopic world emerge from a theory where, apparently, not all <br />
aspects of physical systems are objective? The notion of quantum <br />
Darwinism, put forward and popularized by Wojciech Zurek, is a path in <br />
that direction. In this talk I will discuss the main ideas behind <br />
quantum Darwinism, explore it in some simple models, and briefly discuss <br />
its relationship (or the lack of it) with the notion of non-Markovianity <br />
of quantum dynamical systems.<br />
<br />
<br />
----<br />
----<br />
<br />
=== Thursday, Nov 21th, 2019, 12:30 - 1:30 pm in Keck 370, refreshments from 12:15 (same room) ===<br />
<br />
==== ''Speaker:'' '''Sandu Popescu, University of Bristol, UK''' ====<br />
''Title:'' '''Exploring the limits of no-backward-in-time signaling'''<br />
<br />
''Abstract:'' One of the most routine observations that we make about our world is that we cannot signal backwards in time. So ubiquitous is this understanding that it is often taken as one of the basic laws of Nature. At first glance, this remark seems straightforward. However, as I will show, in probabilistic theories such as quantum mechanics, the consequences of such an assertion are far more involved. In fact, we will see that there is a surprising amount of liberty: some theories even allow the future to affect the past, nevertheless without signaling backwards in time.<br />
<br />
<br />
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----<br />
<br />
=== Friday, Nov 8th, 2019, 3 - 4 pm in Keck 171, refreshments from 2:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Fredrik Dahlqvist, University College London, UK''' ====<br />
<br />
''Title:'' '''A probabilistic approach to floating point arithmetic'''<br />
<br />
''Abstract:'' Finite-precision floating point arithmetic introduces rounding errors which are traditionally bounded using a worst-case analysis. However, worst-case analysis might be overly conservative because worst-case errors can be extremely rare events in practice. Here we develop a probabilistic model of rounding errors with which it becomes possible to quantify the likelihood that the rounding error of an algorithm lies within a given interval. <br />
<br />
Given an input distribution, the model requires the distribution of rounding errors. We show how to exactly compute this distribution for low precision arithmetic. For high precision arithmetic we derive a simple but surprisingly useful approximation. The model is then entirely compositional: given a numerical program written in a simple imperative programing language we can recursively compute the distribution of rounding errors at each step and propagate it through each program instruction. This is done by applying a formalism originaly developed by Kozen to understand the semantics of probabilistic programs, for example how probability distributions gets transformed by assignments or "if then else" statements.<br />
<br />
<br />
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----<br />
<br />
=== Wednesday, Nov 6th, 2019, 4 - 5 pm in Keck 370, refreshments from 3:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Jacques Pienaar, International Institute of Physics in Natal, Brazil''' ====<br />
<br />
''Title:'' '''The new question in quantum foundations: what is causality?'''<br />
<br />
''Abstract:'' Work in quantum foundations has tended to concentrate on Bell's Theorem, <br />
but recently a particular aspect of that theorem has taken on a life of <br />
its own: the question of what "causality" means in quantum mechanics, <br />
and how to model it. This movement has been driven in large part by <br />
recent advances in causal modeling in the statistical and Artificial <br />
Intelligence communities, which have had a heavy influence on quantum <br />
causal modeling. These "classical" approaches tend to define causality <br />
as a probabilistic and action-centered concept, which fits well with <br />
modern information-theoretic treatments of quantum mechanics. However, <br />
the classical approaches also tend to emphasize notions of underlying <br />
determinism and objective mechanisms that do not sit so well in the <br />
quantum context. In this talk I will step back from most of the <br />
technical jargon and try to get to the heart of some of the conceptual <br />
issues involved in "quantizing" the concept of causality, critically <br />
reviewing some key findings, pointing out potential inconsistencies and <br />
outlining possible directions for further inquiry into this fascinating <br />
problem.<br />
<br />
<br />
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----<br />
<br />
=== Friday, October 18th, 2019, 12 - 1 pm in Keck 370, refreshments from 11:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Prof. Lev Vaidman, Alex Maguy-Glass Chair in Physics of Complex Systems, Tel Aviv University, Israel''' ====<br />
<br />
''Title:'' '''The past of a quantum particle'''<br />
<br />
''Abstract:'' Textbooks of quantum mechanics lack the concept of the past of quantum systems. Few years ago I proposed to define the past of a quantum particle according to the trace it leaves. While in many cases this definition provides a reasonable description, for a nested Mach-Zehnder interferometer it leads to a picture seemingly contradicting common sense: the particle leaves a trace in a place through which it could not pass. I will discuss recent theoretical and experimental studies of this controversial issue.<br />
<br />
<br />
----<br />
----<br />
<br />
=== Friday, October 11th, 2019, 1 - 2 pm in Keck 370, refreshments from 12:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Prof. Thomas Curtright, University of Miami''' ====<br />
<br />
''Title:'' '''Massive Dual Gravity Revisited'''<br />
<br />
''Abstract:'' I will describe a highly speculative model of gravity as a massive,<br />
pure spin 2 field, which is "dual" to the usual description in terms of<br />
a spacetime metric tensor.<br />
<br />
In the dual description, for weak fields, the metric emerges as the<br />
field strength of an underlying fundamental field. More generally, if<br />
the gravitational field is not weak, the metric emerges as a nonlinear<br />
mixture involving the energy momentum tensor.<br />
<br />
<br />
----<br />
----<br />
<br />
=== Wednesday, October 9th, 2019, 4 - 5 pm in Keck 370, refreshments from 3:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Alain Hénaut, Institut de Mathématiques de Bordeaux, Université de Bordeaux, France''' ====<br />
<br />
''Title:'' '''On planar web geometry'''<br />
<br />
''Abstract:'' Web geometry deals with foliations in general position. In the planar case and the complex setting, a $d$-web is given by the generic family of integral curves of an analytic or an algebraic differential equation $F(x,y,y')=0$ with $y'$-degree $d$. Invariants of these configurations as abelian relations (related to Abel's addition theorem), Lie symmetries or Godbillon-Vey sequences are investigated. This viewpoint enlarges the qualitative study of differential equations and their moduli. In the nonsingular case and through the singularities, Cartan-Spencer and meromorphic connections methods will be used. Basic examples will be given from different domains including classic algebraic geometry and WDVV-equations. Standard results and open problems will be mentioned. Illustration of the interplay between differential and algebraic geometry, new results will be presented. <br />
<br />
<br />
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----<br />
<br />
=== Thursday, September 5th, 2019, 4 - 5 pm in Keck 171, refreshments from 3:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Nicole Yunger Halpern, Harvard-Smithsonian ITAMP (Institute for Theoretical Atomic, Molecular, and Optical Physics) Harvard University Department of Physics''' ====<br />
<br />
''Title:'' '''Entropic uncertainty relations for quantum-information scrambling'''<br />
<br />
''Abstract:'' How violently do two quantum operators disagree? Different subfields of physics feature different notions of incompatibility: (i) In quantum information theory, uncertainty relations are cast in terms of entropies. These entropic uncertainty relations constrain measurement outcomes. (ii) Condensed matter and high-energy physics feature interacting quantum many-body systems, such as spin chains. A local perturbation, such as a Pauli operator on one side of a chain, spreads through many-body entanglement. The perturbation comes to overlap, and to disagree, with probes localized on the opposite side of the system. This disagreement signals that quantum information about the perturbation has scrambled, or become hidden in highly nonlocal correlations. I will unite these two notions of quantum operator disagreement, presenting an entropic uncertainty relation for quantum-information scrambling. The entropies are of distributions over weak and strong measurements’ possible outcomes. The uncertainty bound strengthens when a spin chain scrambles in numerical simulations. Hence the subfields—quantum information, condensed matter, and high-energy physics—can agree about when quantum operations disagree. Our relation can be tested experimentally with superconducting qubits, trapped ions, and quantum dots.<br />
<br />
NYH, Bartolotta, and Pollack, Comms. Phys. 2, 92 (2019). https://www.nature.com/articles/s42005-019-0179-8<br />
<br />
<br />
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----<br />
<br />
=== Monday, August 26, 2019, 7 - 8:30 pm, in Argyros Forum, Room 209 A&B, networking from 6:15 to 7pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Frederick Eberhardt, Professor of Philosophy in the Division of the Humanities and Social Sciences at the California Institute of Technology''' ====<br />
<br />
''Title:'' '''Computing Causal Relations at Scale or Causality: From Aristotle through Computing to Zebrafish'''<br />
<br />
''Abstract:'' What causes what? How do we untangle the “why” behind processes that regulate the brain, the climate or the economy? If “Correlation does not imply causation" is the standard mantra in science, how can we ever discover causal relationships behind the data? Will it ever be possible for intelligent AI to make its own deductions and predictions? In recent years researchers have developed mathematical techniques that give us the power to infer the underlying “why” behind scientific data. What’s more, we’ve learned that we can discover these causes without performing experiments. Starting with a little practical example with lightbulbs that can be worked out by hand we will see how the problem scales as the number of variables increases. To compute the neural connections in a zebrafish brain, high performance computing is essential.<br />
<br />
''Bio:'' Frederick Eberhardt is Professor of Philosophy in the Division of the Humanities and Social Sciences at the California Institute of Technology. Before coming to Caltech he was Assistant Professor in the Philosophy-Neuroscience-Psychology (PNP) program and the Department of Philosophy at Washington University in St. Louis and a postdoc at the Institute of Cognitive and Brain Sciences at the University of California, Berkeley. As an undergraduate he attended the London School of Economics for a Bachelor in Philosophy & Mathematics. He received his PhD in philosophy from Carnegie Mellon University, where he also completed a Masters in Machine Learning.<br />
<br />
His research interests lie at the intersection of philosophy of science, machine learning and statistics. He is particularly interested in the development of methods for causal discovery from statistical data.<br />
<br />
<br />
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<br />
<br />
<br />
== Previous Seminar talks ==<br />
<br />
* [[MPC Seminar 2019]]<br />
<br />
* [[MPC Seminar 2018]]<br />
<br />
* [[MathCS Seminar 2017]]<br />
<br />
* [[MathCS Seminar 2016]]<br />
<br />
* [[MathCS Seminar 2015]]<br />
<br />
* [[MathCS Seminar 2014]]<br />
<br />
* [[MathCS Seminar 2013]]<br />
<br />
* [[MathCS Seminar 2012]]<br />
<br />
* [[MathCS Seminar 2011]]<br />
<br />
* [[MathCS Seminar 2010]]<br />
<br />
* [[MathCS Seminar 2009]]<br />
<br />
* [[MathCS Seminar 2008]]<br />
<br />
* [[MathCS Seminar 2007]]<br />
<br />
* [[MathCS Seminar 2006]]<br />
<br />
* [[MathCS Seminar 2005]]<br />
<br />
* [[MathCS Seminar 2004]]<br />
<br />
* [[MathCS Seminar 2003]]<br />
<br />
* [[MathCS Seminar 2002]]</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=MPC_Seminar&diff=26MPC Seminar2021-09-15T00:45:45Z<p>Jipsen: /* Spring 2021 */</p>
<hr />
<div>This is the homepage of the Chapman University '''Mathematics, Physics, and Computation Seminars'''<br />
([[MPC Seminar]])<br />
<br />
''Seminar Organizers:'' Roman Buniy and Peter Jipsen<br />
<br />
<br />
== Fall 2021 ==<br />
<br />
The MPC seminar is held in-person in the Keck Center of Science and Engineering, Room 370 (unless a speaker prefers to hold the talk over Zoom). The date and time are included in the announcements below.<br />
<br />
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<br />
== Spring 2021 ==<br />
<br />
<br />
=== Monday, May 3rd, 2021, 1 - 2 pm on Zoom ===<br />
<br />
==== ''Speaker:'' '''Simon Henry, University of Ottawa''' ====<br />
<br />
''Title:'' '''Localic C*-algebras and the Geometric Bohr topos'''<br />
<br />
''Abstract:'' The Bohr topos is a space attached to a C*-algebra A that has been introduced in the hope of producing a new point of view on the mathematics of Quantum mechanics. It is essentially the "space of commutative sub-C*-algebra of A". But its original construction had two problems: (1) it had "the wrong topology" and (2) it was a "non-geometric" construction, i.e. when applied to continuous families of C*-algebras, it wasn't compatible with certain change-of-base functors. In this talk I'll explain how the theory of localic C*-algebras and some classical idea from "geometric logic" allows to give a new version of this construction that solves both of these problems.<br />
<br />
''Link to paper:'' [https://arxiv.org/pdf/1502.01896.pdf arxiv.org/pdf/1502.01896.pdf]<br />
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<br />
<br />
=== Thursday, Jan 21st, 2021, 4 - 5 pm on Zoom ===<br />
<br />
==== ''Speaker:'' '''Mike Campbell, Eureka (SAP), joint work with Vernon Smith (Chapman University)''' ====<br />
<br />
''Title:'' '''An Elementary Humanomics Approach to Boundedly Rational Quadratic Models'''<br />
<br />
''Video of talk:'' [https://youtu.be/F74RlCAjC_A YouTube] ''Slides:'' [http://math.chapman.edu/~jipsen/seminarposters/MikeCampbell2021HumanomicsApproachBRQuadratic.pdf pdf]<br />
<br />
''Abstract:'' We take a refreshing new look at boundedly rational quadratic models in economics using some elementary modeling of the principles put forward in the book Humanomics by Vernon L. Smith and Bart J. Wilson. A simple model is introduced built on the fundamental Humanomics principles of gratitude/resentment felt and the corresponding action responses of reward/punishment in the form of higher/lower payoff transfers. There are two timescales: one for strictly self-interested action, as in economic equilibrium, and another governed by feelings of gratitude/resentment. One of three timescale scenarios is investigated: one where gratitude/resentment changes much more slowly than economic equilibrium ("quenched model"). Another model, in which economic equilibrium occurs over a much slower time than gratitude/resent evolution ("annealed model") is set up, but not investigated. The quenched model with homogeneous interactions turns out to be a non-frustrated spin-glass model. A two-agent quenched model with heterogeneous aligning (ferromagnetic) interactions is analyzed and yields new insights into the critical quenched probability p (1-p) that represents the empirical frequency of opportunity for agent i to take action for the benefit (hurt) of other that invokes mutual gratitude (resentment). A critical quenched probability p*i, i=1,2, exists for each agent. When p < p*i, agent i will choose action in their self-interest. When p > p*i, agent i will take action sensitive to their interpersonal feelings of gratitude/resentment and thus reward/punish the initiating benefit/hurt. We find that the p*i are greater than one-half, which implies agents are averse to resentful behavior and punishment. This was not built into the model, but is a result of its properties, and consistent with Axiom 4 in Humanomics about the asymmetry of gratitude and resentment. Furthermore, the agent who receives less payoff is more averse to resentful behavior; i.e., has a higher critical quenched probability. For this particular model, the Nash equilibrium has no predictive power of Humanomics properties since the rewards are the same for self-interested behavior, resentful behavior, and gratitude behavior. Accordingly, we see that the boundedly rational Gibbs equilibrium does indeed lead to richer properties.<br />
<br />
''Link to paper:'' [https://digitalcommons.chapman.edu/cgi/viewcontent.cgi?article=1330&context=esi_working_papers Chapman Digital Commons]<br />
<br />
== Spring 2020 ==<br />
<br />
The seminar talks are held in '''Keck Center for Science and Engineering, KC 370''' (Center St. Orange, CA 92866, intersection of Center St. And Sycamore St.), '''usually on Wednesday at 4 pm'''.<br />
Sometimes there will be a change of time or venue and the announcement will reflect this change.<br />
<br />
See [http://www.chapman.edu/about/maps-directions/index.aspx Maps<br />
and directions], Keck Center is Building 28 on the Campus Map [https://www.chapman.edu/about/_files/maps-and-directions/current-maps/campus-map.pdf <br />
Campus map]<br />
<br />
<br />
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----<br />
<br />
<br />
=== Friday, Feb 21st, 2020, noon - 1 pm in Keck 370, refreshments at 11:45 am (same room) ===<br />
<br />
==== ''Speaker:'' '''Christian Williams, University of California at Riverside''' ====<br />
<br />
''Title:'' '''Predicate Calculus for Algebraic Theories'''<br />
<br />
''Abstract:'' There is a notion of predicate for algebraic theories, which admits a calculus of both logical and algebraic operations. We thereby extend equational logic by first-order logic, and provide a natural type theory for algebraic structures.<br />
<br />
We demonstrate the idea with the theory of monoids, and derive the example predicate "prime". This and many algebraic examples are only useful when they are mapped from a theory into actual models. There is much to be done in this direction. However, the driving motivation of this work is the application to programming languages: we focus on applying the idea to a more general notion of theory with variable binding.<br />
<br />
The construction is given in the topos of presheaves on a theory T: a "predicate" is a sieve on an object t of T, which corresponds to a subfunctor of the representable T(-,t). For each type t, these predicates form a Heyting algebra, providing the constructors of intuitionistic logic. The operations of T can be lifted to act on predicates, and we construct a model Pred(T): T -->HeyAlg. The correspondence between the operations of T and those in the image of Pred(T) gives that the former are "polymorphic" with respect to the types of the latter. This process can be understood as providing the theory T with a polymorphic type system.<br />
<br />
The original motivation of this work is a logic for concurrency known as Namespace Logic. This applies to the reflective higher-order pi calculus, which is the language of the distributed computing platform RChain. We demonstrate the above framework by constructing namespace logic. This gives a glimpse into a large field of potential application.<br />
<br />
[http://math.chapman.edu/~jipsen/seminarposters/Christian_Williams_pcat_2020-02-21.pdf Slides from the talk]<br />
<br />
<br />
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<br />
=== Wednesday, Feb 19th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Simon Cho, University of Michigan''' ====<br />
''Title:'' '''A categorical perspective on persistent and magnitude homology'''<br />
<br />
''Abstract:'' We define and explain both persistent homology and magnitude homology, and their respective roles in applications (in both pure and applied settings). We will exhibit how both arise as a "singular complex" of a metric space in essentially the same way, but for different values of a parameter.<br />
<br />
<br />
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<br />
=== Wednesday, Feb 12th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Stephon Alexander, Brown University, Rhode Island''' ====<br />
''Title:'' '''The Quantum Cosmological Constant'''<br />
<br />
''Abstract:'' The mysteries surrounding the Cosmological Constant presides at the interface of quantum mechanics and gravity. In this seminar,<br />
I will provide a pedagogical discussion of the many faces of the cosmological constant problem and discuss some current research that<br />
paves new directions that invites us to rethink the quantum nature of vacuum energy.<br />
<br />
<br />
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<br />
=== Tuesday, Jan 14th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Pedram Roushan, Google Inc., Santa Barbara, CA''' ====<br />
''Title:'' '''Quantum supremacy using a programmable superconducting processor'''<br />
<br />
''Abstract:'' The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor1. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 2^53 (about 10^16). Measurements from repeated experiments sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 seconds to sample one instance of a quantum circuit a million times—our benchmarks currently indicate that the equivalent task for a state-of-the-art classical supercomputer would take approximately 10,000 years. This dramatic increase in speed compared to all known classical algorithms is an experimental realization of quantum supremacy for this specific computational task, heralding a much-anticipated computing paradigm. If time permits, I will present some of our more recent measurements. <br />
<br />
<br />
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----<br />
<br />
== Fall 2019 ==<br />
<br />
The seminar talks are held in '''Keck Center for Science and Engineering, KC 370''' (Center St. Orange, CA 92866, intersection of Center St. And Sycamore St.), '''usually on Wednesday at 4 pm'''.<br />
Sometimes there will be a change of time or venue and the announcement will reflect this change.<br />
<br />
See [http://www.chapman.edu/about/maps-directions/index.aspx Maps<br />
and directions], Keck Center is Building 28 on the Campus Map [https://www.chapman.edu/about/_files/maps-and-directions/current-maps/campus-map.pdf <br />
Campus map]<br />
<br />
<br />
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----<br />
<br />
=== Thursday, Dec 12th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Alí Guzmán Adán, Universiteit Gent, Belgium''' ====<br />
''Title:'' '''Pizzetti and Cauchy formulae for higher dimensional surfaces: a<br />
distributional approach'''<br />
<br />
''Abstract:'' In this talk, we study Pizzetti-type formulas for Stiefel<br />
manifolds and Cauchy-type formulas for the tangential Dirac operator<br />
from a distributional perspective. First, we illustrate a general<br />
distributional method for integration over manifolds in R^m defined by<br />
means of k equations. We apply this method to derive an alternative<br />
proof of the Pizzetti formulae for the real Stiefel manifolds<br />
SO(m)/SO(m-k). Besides, a distributional interpretation of invariant<br />
oriented integration is provided. In particular, we obtain a<br />
distributional Cauchy theorem for the tangential Dirac operator on an<br />
embedded (m-k)-dimensional smooth surface.<br />
<br />
<br />
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----<br />
<br />
=== Wednesday, Dec 11th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Arjendu K Pattanayak, Physics and Astronomy, Carleton College, Northfield, Minnesota''' ====<br />
''Title:'' '''Quantum entanglement and tunneling oscillations in a (few) many-body nonlinear spin system'''<br />
<br />
''Abstract:'' Quantum tunnelling permits recoherence or refocusing in real or phase space after the initial quantum state has seemingly delocalized, exhibiting so-called classically forbidden dynamics. For a nonlinearly interacting many-body spin system this interim state can be an entangled state. We report on recent results from investigations into this phenomenon for initially spin coherent pure states in the paradigmatic kicked top (vale Haake) system. This has a mixed regualar and chaotic phase space in the classical limit and exhibits the entanglement tunneling described above, including coherent dynamics between phase-space stability islands; here the interim state is maximally entangled. We map the dependence on various parameters including nonlinear spin and number of spins involved (focusing mostly on the remarkable special case N=4) using a metric that attempts to quantify the quality and rate of tunnelling. The calculations of tunneling rates using eigenvalues and eigenstates of the time evolution operator as a function of initial condition compared to classical space structures demonstrates several nontrivial ways in which quantum behavior transitions to classical as the size of the system grows.<br />
<br />
<br />
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----<br />
<br />
=== Wednesday, Dec 4th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Raphael Drumond, Universidade Federal de Minas Gerais, Brazil''' ====<br />
''Title:'' '''The basics of Quantum Darwinism (and its relationship with non-Markovianity)'''<br />
<br />
''Abstract:'' Some aspects of physical systems described by quantum <br />
mechanics, most notably the possibility of violating a Bell inequality, <br />
suggests (to some) or unavoidably implies (to others) that certain <br />
properties of microscopic systems, like the precise values of position <br />
and momentum of a fundamental particle, do not have an objective <br />
reality. This strongly contrasts with the objectivity of properties of <br />
everyday macroscopic systems like the (rough estimate of) position and <br />
momentum of a baseball. Now, how can this objectivity of the <br />
macroscopic world emerge from a theory where, apparently, not all <br />
aspects of physical systems are objective? The notion of quantum <br />
Darwinism, put forward and popularized by Wojciech Zurek, is a path in <br />
that direction. In this talk I will discuss the main ideas behind <br />
quantum Darwinism, explore it in some simple models, and briefly discuss <br />
its relationship (or the lack of it) with the notion of non-Markovianity <br />
of quantum dynamical systems.<br />
<br />
<br />
----<br />
----<br />
<br />
=== Thursday, Nov 21th, 2019, 12:30 - 1:30 pm in Keck 370, refreshments from 12:15 (same room) ===<br />
<br />
==== ''Speaker:'' '''Sandu Popescu, University of Bristol, UK''' ====<br />
''Title:'' '''Exploring the limits of no-backward-in-time signaling'''<br />
<br />
''Abstract:'' One of the most routine observations that we make about our world is that we cannot signal backwards in time. So ubiquitous is this understanding that it is often taken as one of the basic laws of Nature. At first glance, this remark seems straightforward. However, as I will show, in probabilistic theories such as quantum mechanics, the consequences of such an assertion are far more involved. In fact, we will see that there is a surprising amount of liberty: some theories even allow the future to affect the past, nevertheless without signaling backwards in time.<br />
<br />
<br />
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<br />
=== Friday, Nov 8th, 2019, 3 - 4 pm in Keck 171, refreshments from 2:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Fredrik Dahlqvist, University College London, UK''' ====<br />
<br />
''Title:'' '''A probabilistic approach to floating point arithmetic'''<br />
<br />
''Abstract:'' Finite-precision floating point arithmetic introduces rounding errors which are traditionally bounded using a worst-case analysis. However, worst-case analysis might be overly conservative because worst-case errors can be extremely rare events in practice. Here we develop a probabilistic model of rounding errors with which it becomes possible to quantify the likelihood that the rounding error of an algorithm lies within a given interval. <br />
<br />
Given an input distribution, the model requires the distribution of rounding errors. We show how to exactly compute this distribution for low precision arithmetic. For high precision arithmetic we derive a simple but surprisingly useful approximation. The model is then entirely compositional: given a numerical program written in a simple imperative programing language we can recursively compute the distribution of rounding errors at each step and propagate it through each program instruction. This is done by applying a formalism originaly developed by Kozen to understand the semantics of probabilistic programs, for example how probability distributions gets transformed by assignments or "if then else" statements.<br />
<br />
<br />
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<br />
=== Wednesday, Nov 6th, 2019, 4 - 5 pm in Keck 370, refreshments from 3:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Jacques Pienaar, International Institute of Physics in Natal, Brazil''' ====<br />
<br />
''Title:'' '''The new question in quantum foundations: what is causality?'''<br />
<br />
''Abstract:'' Work in quantum foundations has tended to concentrate on Bell's Theorem, <br />
but recently a particular aspect of that theorem has taken on a life of <br />
its own: the question of what "causality" means in quantum mechanics, <br />
and how to model it. This movement has been driven in large part by <br />
recent advances in causal modeling in the statistical and Artificial <br />
Intelligence communities, which have had a heavy influence on quantum <br />
causal modeling. These "classical" approaches tend to define causality <br />
as a probabilistic and action-centered concept, which fits well with <br />
modern information-theoretic treatments of quantum mechanics. However, <br />
the classical approaches also tend to emphasize notions of underlying <br />
determinism and objective mechanisms that do not sit so well in the <br />
quantum context. In this talk I will step back from most of the <br />
technical jargon and try to get to the heart of some of the conceptual <br />
issues involved in "quantizing" the concept of causality, critically <br />
reviewing some key findings, pointing out potential inconsistencies and <br />
outlining possible directions for further inquiry into this fascinating <br />
problem.<br />
<br />
<br />
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<br />
=== Friday, October 18th, 2019, 12 - 1 pm in Keck 370, refreshments from 11:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Prof. Lev Vaidman, Alex Maguy-Glass Chair in Physics of Complex Systems, Tel Aviv University, Israel''' ====<br />
<br />
''Title:'' '''The past of a quantum particle'''<br />
<br />
''Abstract:'' Textbooks of quantum mechanics lack the concept of the past of quantum systems. Few years ago I proposed to define the past of a quantum particle according to the trace it leaves. While in many cases this definition provides a reasonable description, for a nested Mach-Zehnder interferometer it leads to a picture seemingly contradicting common sense: the particle leaves a trace in a place through which it could not pass. I will discuss recent theoretical and experimental studies of this controversial issue.<br />
<br />
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<br />
=== Friday, October 11th, 2019, 1 - 2 pm in Keck 370, refreshments from 12:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Prof. Thomas Curtright, University of Miami''' ====<br />
<br />
''Title:'' '''Massive Dual Gravity Revisited'''<br />
<br />
''Abstract:'' I will describe a highly speculative model of gravity as a massive,<br />
pure spin 2 field, which is "dual" to the usual description in terms of<br />
a spacetime metric tensor.<br />
<br />
In the dual description, for weak fields, the metric emerges as the<br />
field strength of an underlying fundamental field. More generally, if<br />
the gravitational field is not weak, the metric emerges as a nonlinear<br />
mixture involving the energy momentum tensor.<br />
<br />
<br />
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<br />
=== Wednesday, October 9th, 2019, 4 - 5 pm in Keck 370, refreshments from 3:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Alain Hénaut, Institut de Mathématiques de Bordeaux, Université de Bordeaux, France''' ====<br />
<br />
''Title:'' '''On planar web geometry'''<br />
<br />
''Abstract:'' Web geometry deals with foliations in general position. In the planar case and the complex setting, a $d$-web is given by the generic family of integral curves of an analytic or an algebraic differential equation $F(x,y,y')=0$ with $y'$-degree $d$. Invariants of these configurations as abelian relations (related to Abel's addition theorem), Lie symmetries or Godbillon-Vey sequences are investigated. This viewpoint enlarges the qualitative study of differential equations and their moduli. In the nonsingular case and through the singularities, Cartan-Spencer and meromorphic connections methods will be used. Basic examples will be given from different domains including classic algebraic geometry and WDVV-equations. Standard results and open problems will be mentioned. Illustration of the interplay between differential and algebraic geometry, new results will be presented. <br />
<br />
<br />
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<br />
=== Thursday, September 5th, 2019, 4 - 5 pm in Keck 171, refreshments from 3:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Nicole Yunger Halpern, Harvard-Smithsonian ITAMP (Institute for Theoretical Atomic, Molecular, and Optical Physics) Harvard University Department of Physics''' ====<br />
<br />
''Title:'' '''Entropic uncertainty relations for quantum-information scrambling'''<br />
<br />
''Abstract:'' How violently do two quantum operators disagree? Different subfields of physics feature different notions of incompatibility: (i) In quantum information theory, uncertainty relations are cast in terms of entropies. These entropic uncertainty relations constrain measurement outcomes. (ii) Condensed matter and high-energy physics feature interacting quantum many-body systems, such as spin chains. A local perturbation, such as a Pauli operator on one side of a chain, spreads through many-body entanglement. The perturbation comes to overlap, and to disagree, with probes localized on the opposite side of the system. This disagreement signals that quantum information about the perturbation has scrambled, or become hidden in highly nonlocal correlations. I will unite these two notions of quantum operator disagreement, presenting an entropic uncertainty relation for quantum-information scrambling. The entropies are of distributions over weak and strong measurements’ possible outcomes. The uncertainty bound strengthens when a spin chain scrambles in numerical simulations. Hence the subfields—quantum information, condensed matter, and high-energy physics—can agree about when quantum operations disagree. Our relation can be tested experimentally with superconducting qubits, trapped ions, and quantum dots.<br />
<br />
NYH, Bartolotta, and Pollack, Comms. Phys. 2, 92 (2019). https://www.nature.com/articles/s42005-019-0179-8<br />
<br />
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<br />
=== Monday, August 26, 2019, 7 - 8:30 pm, in Argyros Forum, Room 209 A&B, networking from 6:15 to 7pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Frederick Eberhardt, Professor of Philosophy in the Division of the Humanities and Social Sciences at the California Institute of Technology''' ====<br />
<br />
''Title:'' '''Computing Causal Relations at Scale or Causality: From Aristotle through Computing to Zebrafish'''<br />
<br />
''Abstract:'' What causes what? How do we untangle the “why” behind processes that regulate the brain, the climate or the economy? If “Correlation does not imply causation" is the standard mantra in science, how can we ever discover causal relationships behind the data? Will it ever be possible for intelligent AI to make its own deductions and predictions? In recent years researchers have developed mathematical techniques that give us the power to infer the underlying “why” behind scientific data. What’s more, we’ve learned that we can discover these causes without performing experiments. Starting with a little practical example with lightbulbs that can be worked out by hand we will see how the problem scales as the number of variables increases. To compute the neural connections in a zebrafish brain, high performance computing is essential.<br />
<br />
''Bio:'' Frederick Eberhardt is Professor of Philosophy in the Division of the Humanities and Social Sciences at the California Institute of Technology. Before coming to Caltech he was Assistant Professor in the Philosophy-Neuroscience-Psychology (PNP) program and the Department of Philosophy at Washington University in St. Louis and a postdoc at the Institute of Cognitive and Brain Sciences at the University of California, Berkeley. As an undergraduate he attended the London School of Economics for a Bachelor in Philosophy & Mathematics. He received his PhD in philosophy from Carnegie Mellon University, where he also completed a Masters in Machine Learning.<br />
<br />
His research interests lie at the intersection of philosophy of science, machine learning and statistics. He is particularly interested in the development of methods for causal discovery from statistical data.<br />
<br />
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<br />
<br />
== Previous Seminar talks ==<br />
<br />
* [[MPC Seminar 2019]]<br />
<br />
* [[MPC Seminar 2018]]<br />
<br />
* [[MathCS Seminar 2017]]<br />
<br />
* [[MathCS Seminar 2016]]<br />
<br />
* [[MathCS Seminar 2015]]<br />
<br />
* [[MathCS Seminar 2014]]<br />
<br />
* [[MathCS Seminar 2013]]<br />
<br />
* [[MathCS Seminar 2012]]<br />
<br />
* [[MathCS Seminar 2011]]<br />
<br />
* [[MathCS Seminar 2010]]<br />
<br />
* [[MathCS Seminar 2009]]<br />
<br />
* [[MathCS Seminar 2008]]<br />
<br />
* [[MathCS Seminar 2007]]<br />
<br />
* [[MathCS Seminar 2006]]<br />
<br />
* [[MathCS Seminar 2005]]<br />
<br />
* [[MathCS Seminar 2004]]<br />
<br />
* [[MathCS Seminar 2003]]<br />
<br />
* [[MathCS Seminar 2002]]</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=MPC_Seminar&diff=25MPC Seminar2021-05-02T18:21:14Z<p>Jipsen: Undo revision 24 by Jipsen (talk)</p>
<hr />
<div>This is the homepage of the Chapman University '''Mathematics, Physics, and Computation Seminars'''<br />
([[MPC Seminar]])<br />
<br />
''Seminar Organizers:'' Roman Buniy and Peter Jipsen<br />
<br />
<br />
== Spring 2021 ==<br />
<br />
The MPC seminar is held via Zoom for now. The Zoom address will be sent in the email announcements (email jipsen@chapman.edu if you would like to have your email address added to the mailing list).<br />
<br />
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<br />
<br />
=== Monday, May 3rd, 2021, 1 - 2 pm on Zoom ===<br />
<br />
==== ''Speaker:'' '''Simon Henry, University of Ottawa''' ====<br />
<br />
''Title:'' '''Localic C*-algebras and the Geometric Bohr topos'''<br />
<br />
''Abstract:'' The Bohr topos is a space attached to a C*-algebra A that has been introduced in the hope of producing a new point of view on the mathematics of Quantum mechanics. It is essentially the "space of commutative sub-C*-algebra of A". But its original construction had two problems: (1) it had "the wrong topology" and (2) it was a "non-geometric" construction, i.e. when applied to continuous families of C*-algebras, it wasn't compatible with certain change-of-base functors. In this talk I'll explain how the theory of localic C*-algebras and some classical idea from "geometric logic" allows to give a new version of this construction that solves both of these problems.<br />
<br />
''Link to paper:'' [https://arxiv.org/pdf/1502.01896.pdf arxiv.org/pdf/1502.01896.pdf]<br />
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<br />
<br />
=== Thursday, Jan 21st, 2021, 4 - 5 pm on Zoom ===<br />
<br />
==== ''Speaker:'' '''Mike Campbell, Eureka (SAP), joint work with Vernon Smith (Chapman University)''' ====<br />
<br />
''Title:'' '''An Elementary Humanomics Approach to Boundedly Rational Quadratic Models'''<br />
<br />
''Video of talk:'' [https://youtu.be/F74RlCAjC_A YouTube] ''Slides:'' [http://math.chapman.edu/~jipsen/seminarposters/MikeCampbell2021HumanomicsApproachBRQuadratic.pdf pdf]<br />
<br />
''Abstract:'' We take a refreshing new look at boundedly rational quadratic models in economics using some elementary modeling of the principles put forward in the book Humanomics by Vernon L. Smith and Bart J. Wilson. A simple model is introduced built on the fundamental Humanomics principles of gratitude/resentment felt and the corresponding action responses of reward/punishment in the form of higher/lower payoff transfers. There are two timescales: one for strictly self-interested action, as in economic equilibrium, and another governed by feelings of gratitude/resentment. One of three timescale scenarios is investigated: one where gratitude/resentment changes much more slowly than economic equilibrium ("quenched model"). Another model, in which economic equilibrium occurs over a much slower time than gratitude/resent evolution ("annealed model") is set up, but not investigated. The quenched model with homogeneous interactions turns out to be a non-frustrated spin-glass model. A two-agent quenched model with heterogeneous aligning (ferromagnetic) interactions is analyzed and yields new insights into the critical quenched probability p (1-p) that represents the empirical frequency of opportunity for agent i to take action for the benefit (hurt) of other that invokes mutual gratitude (resentment). A critical quenched probability p*i, i=1,2, exists for each agent. When p < p*i, agent i will choose action in their self-interest. When p > p*i, agent i will take action sensitive to their interpersonal feelings of gratitude/resentment and thus reward/punish the initiating benefit/hurt. We find that the p*i are greater than one-half, which implies agents are averse to resentful behavior and punishment. This was not built into the model, but is a result of its properties, and consistent with Axiom 4 in Humanomics about the asymmetry of gratitude and resentment. Furthermore, the agent who receives less payoff is more averse to resentful behavior; i.e., has a higher critical quenched probability. For this particular model, the Nash equilibrium has no predictive power of Humanomics properties since the rewards are the same for self-interested behavior, resentful behavior, and gratitude behavior. Accordingly, we see that the boundedly rational Gibbs equilibrium does indeed lead to richer properties.<br />
<br />
''Link to paper:'' [https://digitalcommons.chapman.edu/cgi/viewcontent.cgi?article=1330&context=esi_working_papers Chapman Digital Commons]<br />
<br />
== Spring 2020 ==<br />
<br />
The seminar talks are held in '''Keck Center for Science and Engineering, KC 370''' (Center St. Orange, CA 92866, intersection of Center St. And Sycamore St.), '''usually on Wednesday at 4 pm'''.<br />
Sometimes there will be a change of time or venue and the announcement will reflect this change.<br />
<br />
See [http://www.chapman.edu/about/maps-directions/index.aspx Maps<br />
and directions], Keck Center is Building 28 on the Campus Map [https://www.chapman.edu/about/_files/maps-and-directions/current-maps/campus-map.pdf <br />
Campus map]<br />
<br />
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<br />
=== Friday, Feb 21st, 2020, noon - 1 pm in Keck 370, refreshments at 11:45 am (same room) ===<br />
<br />
==== ''Speaker:'' '''Christian Williams, University of California at Riverside''' ====<br />
<br />
''Title:'' '''Predicate Calculus for Algebraic Theories'''<br />
<br />
''Abstract:'' There is a notion of predicate for algebraic theories, which admits a calculus of both logical and algebraic operations. We thereby extend equational logic by first-order logic, and provide a natural type theory for algebraic structures.<br />
<br />
We demonstrate the idea with the theory of monoids, and derive the example predicate "prime". This and many algebraic examples are only useful when they are mapped from a theory into actual models. There is much to be done in this direction. However, the driving motivation of this work is the application to programming languages: we focus on applying the idea to a more general notion of theory with variable binding.<br />
<br />
The construction is given in the topos of presheaves on a theory T: a "predicate" is a sieve on an object t of T, which corresponds to a subfunctor of the representable T(-,t). For each type t, these predicates form a Heyting algebra, providing the constructors of intuitionistic logic. The operations of T can be lifted to act on predicates, and we construct a model Pred(T): T -->HeyAlg. The correspondence between the operations of T and those in the image of Pred(T) gives that the former are "polymorphic" with respect to the types of the latter. This process can be understood as providing the theory T with a polymorphic type system.<br />
<br />
The original motivation of this work is a logic for concurrency known as Namespace Logic. This applies to the reflective higher-order pi calculus, which is the language of the distributed computing platform RChain. We demonstrate the above framework by constructing namespace logic. This gives a glimpse into a large field of potential application.<br />
<br />
[http://math.chapman.edu/~jipsen/seminarposters/Christian_Williams_pcat_2020-02-21.pdf Slides from the talk]<br />
<br />
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<br />
=== Wednesday, Feb 19th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Simon Cho, University of Michigan''' ====<br />
''Title:'' '''A categorical perspective on persistent and magnitude homology'''<br />
<br />
''Abstract:'' We define and explain both persistent homology and magnitude homology, and their respective roles in applications (in both pure and applied settings). We will exhibit how both arise as a "singular complex" of a metric space in essentially the same way, but for different values of a parameter.<br />
<br />
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<br />
=== Wednesday, Feb 12th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Stephon Alexander, Brown University, Rhode Island''' ====<br />
''Title:'' '''The Quantum Cosmological Constant'''<br />
<br />
''Abstract:'' The mysteries surrounding the Cosmological Constant presides at the interface of quantum mechanics and gravity. In this seminar,<br />
I will provide a pedagogical discussion of the many faces of the cosmological constant problem and discuss some current research that<br />
paves new directions that invites us to rethink the quantum nature of vacuum energy.<br />
<br />
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<br />
=== Tuesday, Jan 14th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Pedram Roushan, Google Inc., Santa Barbara, CA''' ====<br />
''Title:'' '''Quantum supremacy using a programmable superconducting processor'''<br />
<br />
''Abstract:'' The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor1. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 2^53 (about 10^16). Measurements from repeated experiments sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 seconds to sample one instance of a quantum circuit a million times—our benchmarks currently indicate that the equivalent task for a state-of-the-art classical supercomputer would take approximately 10,000 years. This dramatic increase in speed compared to all known classical algorithms is an experimental realization of quantum supremacy for this specific computational task, heralding a much-anticipated computing paradigm. If time permits, I will present some of our more recent measurements. <br />
<br />
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<br />
== Fall 2019 ==<br />
<br />
The seminar talks are held in '''Keck Center for Science and Engineering, KC 370''' (Center St. Orange, CA 92866, intersection of Center St. And Sycamore St.), '''usually on Wednesday at 4 pm'''.<br />
Sometimes there will be a change of time or venue and the announcement will reflect this change.<br />
<br />
See [http://www.chapman.edu/about/maps-directions/index.aspx Maps<br />
and directions], Keck Center is Building 28 on the Campus Map [https://www.chapman.edu/about/_files/maps-and-directions/current-maps/campus-map.pdf <br />
Campus map]<br />
<br />
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<br />
=== Thursday, Dec 12th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Alí Guzmán Adán, Universiteit Gent, Belgium''' ====<br />
''Title:'' '''Pizzetti and Cauchy formulae for higher dimensional surfaces: a<br />
distributional approach'''<br />
<br />
''Abstract:'' In this talk, we study Pizzetti-type formulas for Stiefel<br />
manifolds and Cauchy-type formulas for the tangential Dirac operator<br />
from a distributional perspective. First, we illustrate a general<br />
distributional method for integration over manifolds in R^m defined by<br />
means of k equations. We apply this method to derive an alternative<br />
proof of the Pizzetti formulae for the real Stiefel manifolds<br />
SO(m)/SO(m-k). Besides, a distributional interpretation of invariant<br />
oriented integration is provided. In particular, we obtain a<br />
distributional Cauchy theorem for the tangential Dirac operator on an<br />
embedded (m-k)-dimensional smooth surface.<br />
<br />
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<br />
=== Wednesday, Dec 11th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Arjendu K Pattanayak, Physics and Astronomy, Carleton College, Northfield, Minnesota''' ====<br />
''Title:'' '''Quantum entanglement and tunneling oscillations in a (few) many-body nonlinear spin system'''<br />
<br />
''Abstract:'' Quantum tunnelling permits recoherence or refocusing in real or phase space after the initial quantum state has seemingly delocalized, exhibiting so-called classically forbidden dynamics. For a nonlinearly interacting many-body spin system this interim state can be an entangled state. We report on recent results from investigations into this phenomenon for initially spin coherent pure states in the paradigmatic kicked top (vale Haake) system. This has a mixed regualar and chaotic phase space in the classical limit and exhibits the entanglement tunneling described above, including coherent dynamics between phase-space stability islands; here the interim state is maximally entangled. We map the dependence on various parameters including nonlinear spin and number of spins involved (focusing mostly on the remarkable special case N=4) using a metric that attempts to quantify the quality and rate of tunnelling. The calculations of tunneling rates using eigenvalues and eigenstates of the time evolution operator as a function of initial condition compared to classical space structures demonstrates several nontrivial ways in which quantum behavior transitions to classical as the size of the system grows.<br />
<br />
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<br />
=== Wednesday, Dec 4th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Raphael Drumond, Universidade Federal de Minas Gerais, Brazil''' ====<br />
''Title:'' '''The basics of Quantum Darwinism (and its relationship with non-Markovianity)'''<br />
<br />
''Abstract:'' Some aspects of physical systems described by quantum <br />
mechanics, most notably the possibility of violating a Bell inequality, <br />
suggests (to some) or unavoidably implies (to others) that certain <br />
properties of microscopic systems, like the precise values of position <br />
and momentum of a fundamental particle, do not have an objective <br />
reality. This strongly contrasts with the objectivity of properties of <br />
everyday macroscopic systems like the (rough estimate of) position and <br />
momentum of a baseball. Now, how can this objectivity of the <br />
macroscopic world emerge from a theory where, apparently, not all <br />
aspects of physical systems are objective? The notion of quantum <br />
Darwinism, put forward and popularized by Wojciech Zurek, is a path in <br />
that direction. In this talk I will discuss the main ideas behind <br />
quantum Darwinism, explore it in some simple models, and briefly discuss <br />
its relationship (or the lack of it) with the notion of non-Markovianity <br />
of quantum dynamical systems.<br />
<br />
<br />
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<br />
=== Thursday, Nov 21th, 2019, 12:30 - 1:30 pm in Keck 370, refreshments from 12:15 (same room) ===<br />
<br />
==== ''Speaker:'' '''Sandu Popescu, University of Bristol, UK''' ====<br />
''Title:'' '''Exploring the limits of no-backward-in-time signaling'''<br />
<br />
''Abstract:'' One of the most routine observations that we make about our world is that we cannot signal backwards in time. So ubiquitous is this understanding that it is often taken as one of the basic laws of Nature. At first glance, this remark seems straightforward. However, as I will show, in probabilistic theories such as quantum mechanics, the consequences of such an assertion are far more involved. In fact, we will see that there is a surprising amount of liberty: some theories even allow the future to affect the past, nevertheless without signaling backwards in time.<br />
<br />
<br />
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<br />
=== Friday, Nov 8th, 2019, 3 - 4 pm in Keck 171, refreshments from 2:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Fredrik Dahlqvist, University College London, UK''' ====<br />
<br />
''Title:'' '''A probabilistic approach to floating point arithmetic'''<br />
<br />
''Abstract:'' Finite-precision floating point arithmetic introduces rounding errors which are traditionally bounded using a worst-case analysis. However, worst-case analysis might be overly conservative because worst-case errors can be extremely rare events in practice. Here we develop a probabilistic model of rounding errors with which it becomes possible to quantify the likelihood that the rounding error of an algorithm lies within a given interval. <br />
<br />
Given an input distribution, the model requires the distribution of rounding errors. We show how to exactly compute this distribution for low precision arithmetic. For high precision arithmetic we derive a simple but surprisingly useful approximation. The model is then entirely compositional: given a numerical program written in a simple imperative programing language we can recursively compute the distribution of rounding errors at each step and propagate it through each program instruction. This is done by applying a formalism originaly developed by Kozen to understand the semantics of probabilistic programs, for example how probability distributions gets transformed by assignments or "if then else" statements.<br />
<br />
<br />
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----<br />
<br />
=== Wednesday, Nov 6th, 2019, 4 - 5 pm in Keck 370, refreshments from 3:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Jacques Pienaar, International Institute of Physics in Natal, Brazil''' ====<br />
<br />
''Title:'' '''The new question in quantum foundations: what is causality?'''<br />
<br />
''Abstract:'' Work in quantum foundations has tended to concentrate on Bell's Theorem, <br />
but recently a particular aspect of that theorem has taken on a life of <br />
its own: the question of what "causality" means in quantum mechanics, <br />
and how to model it. This movement has been driven in large part by <br />
recent advances in causal modeling in the statistical and Artificial <br />
Intelligence communities, which have had a heavy influence on quantum <br />
causal modeling. These "classical" approaches tend to define causality <br />
as a probabilistic and action-centered concept, which fits well with <br />
modern information-theoretic treatments of quantum mechanics. However, <br />
the classical approaches also tend to emphasize notions of underlying <br />
determinism and objective mechanisms that do not sit so well in the <br />
quantum context. In this talk I will step back from most of the <br />
technical jargon and try to get to the heart of some of the conceptual <br />
issues involved in "quantizing" the concept of causality, critically <br />
reviewing some key findings, pointing out potential inconsistencies and <br />
outlining possible directions for further inquiry into this fascinating <br />
problem.<br />
<br />
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<br />
=== Friday, October 18th, 2019, 12 - 1 pm in Keck 370, refreshments from 11:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Prof. Lev Vaidman, Alex Maguy-Glass Chair in Physics of Complex Systems, Tel Aviv University, Israel''' ====<br />
<br />
''Title:'' '''The past of a quantum particle'''<br />
<br />
''Abstract:'' Textbooks of quantum mechanics lack the concept of the past of quantum systems. Few years ago I proposed to define the past of a quantum particle according to the trace it leaves. While in many cases this definition provides a reasonable description, for a nested Mach-Zehnder interferometer it leads to a picture seemingly contradicting common sense: the particle leaves a trace in a place through which it could not pass. I will discuss recent theoretical and experimental studies of this controversial issue.<br />
<br />
<br />
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<br />
=== Friday, October 11th, 2019, 1 - 2 pm in Keck 370, refreshments from 12:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Prof. Thomas Curtright, University of Miami''' ====<br />
<br />
''Title:'' '''Massive Dual Gravity Revisited'''<br />
<br />
''Abstract:'' I will describe a highly speculative model of gravity as a massive,<br />
pure spin 2 field, which is "dual" to the usual description in terms of<br />
a spacetime metric tensor.<br />
<br />
In the dual description, for weak fields, the metric emerges as the<br />
field strength of an underlying fundamental field. More generally, if<br />
the gravitational field is not weak, the metric emerges as a nonlinear<br />
mixture involving the energy momentum tensor.<br />
<br />
<br />
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<br />
=== Wednesday, October 9th, 2019, 4 - 5 pm in Keck 370, refreshments from 3:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Alain Hénaut, Institut de Mathématiques de Bordeaux, Université de Bordeaux, France''' ====<br />
<br />
''Title:'' '''On planar web geometry'''<br />
<br />
''Abstract:'' Web geometry deals with foliations in general position. In the planar case and the complex setting, a $d$-web is given by the generic family of integral curves of an analytic or an algebraic differential equation $F(x,y,y')=0$ with $y'$-degree $d$. Invariants of these configurations as abelian relations (related to Abel's addition theorem), Lie symmetries or Godbillon-Vey sequences are investigated. This viewpoint enlarges the qualitative study of differential equations and their moduli. In the nonsingular case and through the singularities, Cartan-Spencer and meromorphic connections methods will be used. Basic examples will be given from different domains including classic algebraic geometry and WDVV-equations. Standard results and open problems will be mentioned. Illustration of the interplay between differential and algebraic geometry, new results will be presented. <br />
<br />
<br />
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----<br />
<br />
=== Thursday, September 5th, 2019, 4 - 5 pm in Keck 171, refreshments from 3:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Nicole Yunger Halpern, Harvard-Smithsonian ITAMP (Institute for Theoretical Atomic, Molecular, and Optical Physics) Harvard University Department of Physics''' ====<br />
<br />
''Title:'' '''Entropic uncertainty relations for quantum-information scrambling'''<br />
<br />
''Abstract:'' How violently do two quantum operators disagree? Different subfields of physics feature different notions of incompatibility: (i) In quantum information theory, uncertainty relations are cast in terms of entropies. These entropic uncertainty relations constrain measurement outcomes. (ii) Condensed matter and high-energy physics feature interacting quantum many-body systems, such as spin chains. A local perturbation, such as a Pauli operator on one side of a chain, spreads through many-body entanglement. The perturbation comes to overlap, and to disagree, with probes localized on the opposite side of the system. This disagreement signals that quantum information about the perturbation has scrambled, or become hidden in highly nonlocal correlations. I will unite these two notions of quantum operator disagreement, presenting an entropic uncertainty relation for quantum-information scrambling. The entropies are of distributions over weak and strong measurements’ possible outcomes. The uncertainty bound strengthens when a spin chain scrambles in numerical simulations. Hence the subfields—quantum information, condensed matter, and high-energy physics—can agree about when quantum operations disagree. Our relation can be tested experimentally with superconducting qubits, trapped ions, and quantum dots.<br />
<br />
NYH, Bartolotta, and Pollack, Comms. Phys. 2, 92 (2019). https://www.nature.com/articles/s42005-019-0179-8<br />
<br />
<br />
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<br />
=== Monday, August 26, 2019, 7 - 8:30 pm, in Argyros Forum, Room 209 A&B, networking from 6:15 to 7pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Frederick Eberhardt, Professor of Philosophy in the Division of the Humanities and Social Sciences at the California Institute of Technology''' ====<br />
<br />
''Title:'' '''Computing Causal Relations at Scale or Causality: From Aristotle through Computing to Zebrafish'''<br />
<br />
''Abstract:'' What causes what? How do we untangle the “why” behind processes that regulate the brain, the climate or the economy? If “Correlation does not imply causation" is the standard mantra in science, how can we ever discover causal relationships behind the data? Will it ever be possible for intelligent AI to make its own deductions and predictions? In recent years researchers have developed mathematical techniques that give us the power to infer the underlying “why” behind scientific data. What’s more, we’ve learned that we can discover these causes without performing experiments. Starting with a little practical example with lightbulbs that can be worked out by hand we will see how the problem scales as the number of variables increases. To compute the neural connections in a zebrafish brain, high performance computing is essential.<br />
<br />
''Bio:'' Frederick Eberhardt is Professor of Philosophy in the Division of the Humanities and Social Sciences at the California Institute of Technology. Before coming to Caltech he was Assistant Professor in the Philosophy-Neuroscience-Psychology (PNP) program and the Department of Philosophy at Washington University in St. Louis and a postdoc at the Institute of Cognitive and Brain Sciences at the University of California, Berkeley. As an undergraduate he attended the London School of Economics for a Bachelor in Philosophy & Mathematics. He received his PhD in philosophy from Carnegie Mellon University, where he also completed a Masters in Machine Learning.<br />
<br />
His research interests lie at the intersection of philosophy of science, machine learning and statistics. He is particularly interested in the development of methods for causal discovery from statistical data.<br />
<br />
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<br />
<br />
<br />
== Previous Seminar talks ==<br />
<br />
* [[MPC Seminar 2019]]<br />
<br />
* [[MPC Seminar 2018]]<br />
<br />
* [[MathCS Seminar 2017]]<br />
<br />
* [[MathCS Seminar 2016]]<br />
<br />
* [[MathCS Seminar 2015]]<br />
<br />
* [[MathCS Seminar 2014]]<br />
<br />
* [[MathCS Seminar 2013]]<br />
<br />
* [[MathCS Seminar 2012]]<br />
<br />
* [[MathCS Seminar 2011]]<br />
<br />
* [[MathCS Seminar 2010]]<br />
<br />
* [[MathCS Seminar 2009]]<br />
<br />
* [[MathCS Seminar 2008]]<br />
<br />
* [[MathCS Seminar 2007]]<br />
<br />
* [[MathCS Seminar 2006]]<br />
<br />
* [[MathCS Seminar 2005]]<br />
<br />
* [[MathCS Seminar 2004]]<br />
<br />
* [[MathCS Seminar 2003]]<br />
<br />
* [[MathCS Seminar 2002]]</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=MPC_Seminar&diff=24MPC Seminar2021-05-02T18:19:37Z<p>Jipsen: </p>
<hr />
<div>This is the homepage of the Chapman University '''Mathematics, Physics, and Computation Seminars'''<br />
([[MPC Seminar]])<br />
<br />
''Seminar Organizers:'' Roman Buniy and Peter Jipsen<br />
<br />
<br />
== Spring 2021 ==<br />
<br />
The MPC seminar is held via Zoom for now. The Zoom address will be sent in the email announcements.<br />
<br />
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<br />
<br />
=== Monday, May 3rd, 2021, 1 - 2 pm on Zoom ===<br />
<br />
==== ''Speaker:'' '''Simon Henry, University of Ottawa''' ====<br />
<br />
''Title:'' '''Localic C*-algebras and the Geometric Bohr topos'''<br />
<br />
''Abstract:'' The Bohr topos is a space attached to a C*-algebra A that has been introduced in the hope of producing a new point of view on the mathematics of Quantum mechanics. It is essentially the "space of commutative sub-C*-algebra of A". But its original construction had two problems: (1) it had "the wrong topology" and (2) it was a "non-geometric" construction, i.e. when applied to continuous families of C*-algebras, it wasn't compatible with certain change-of-base functors. In this talk I'll explain how the theory of localic C*-algebras and some classical idea from "geometric logic" allows to give a new version of this construction that solves both of these problems.<br />
<br />
''Link to paper:'' [https://arxiv.org/pdf/1502.01896.pdf]<br />
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<br />
<br />
=== Thursday, Jan 21st, 2021, 4 - 5 pm on Zoom ===<br />
<br />
==== ''Speaker:'' '''Mike Campbell, Eureka (SAP), joint work with Vernon Smith (Chapman University)''' ====<br />
<br />
''Title:'' '''An Elementary Humanomics Approach to Boundedly Rational Quadratic Models'''<br />
<br />
''Video of talk:'' [https://youtu.be/F74RlCAjC_A YouTube] ''Slides:'' [http://math.chapman.edu/~jipsen/seminarposters/MikeCampbell2021HumanomicsApproachBRQuadratic.pdf pdf]<br />
<br />
''Abstract:'' We take a refreshing new look at boundedly rational quadratic models in economics using some elementary modeling of the principles put forward in the book Humanomics by Vernon L. Smith and Bart J. Wilson. A simple model is introduced built on the fundamental Humanomics principles of gratitude/resentment felt and the corresponding action responses of reward/punishment in the form of higher/lower payoff transfers. There are two timescales: one for strictly self-interested action, as in economic equilibrium, and another governed by feelings of gratitude/resentment. One of three timescale scenarios is investigated: one where gratitude/resentment changes much more slowly than economic equilibrium ("quenched model"). Another model, in which economic equilibrium occurs over a much slower time than gratitude/resent evolution ("annealed model") is set up, but not investigated. The quenched model with homogeneous interactions turns out to be a non-frustrated spin-glass model. A two-agent quenched model with heterogeneous aligning (ferromagnetic) interactions is analyzed and yields new insights into the critical quenched probability p (1-p) that represents the empirical frequency of opportunity for agent i to take action for the benefit (hurt) of other that invokes mutual gratitude (resentment). A critical quenched probability p*i, i=1,2, exists for each agent. When p < p*i, agent i will choose action in their self-interest. When p > p*i, agent i will take action sensitive to their interpersonal feelings of gratitude/resentment and thus reward/punish the initiating benefit/hurt. We find that the p*i are greater than one-half, which implies agents are averse to resentful behavior and punishment. This was not built into the model, but is a result of its properties, and consistent with Axiom 4 in Humanomics about the asymmetry of gratitude and resentment. Furthermore, the agent who receives less payoff is more averse to resentful behavior; i.e., has a higher critical quenched probability. For this particular model, the Nash equilibrium has no predictive power of Humanomics properties since the rewards are the same for self-interested behavior, resentful behavior, and gratitude behavior. Accordingly, we see that the boundedly rational Gibbs equilibrium does indeed lead to richer properties.<br />
<br />
''Link to paper:'' [https://digitalcommons.chapman.edu/cgi/viewcontent.cgi?article=1330&context=esi_working_papers Chapman Digital Commons]<br />
<br />
== Spring 2020 ==<br />
<br />
The seminar talks are held in '''Keck Center for Science and Engineering, KC 370''' (Center St. Orange, CA 92866, intersection of Center St. And Sycamore St.), '''usually on Wednesday at 4 pm'''.<br />
Sometimes there will be a change of time or venue and the announcement will reflect this change.<br />
<br />
See [http://www.chapman.edu/about/maps-directions/index.aspx Maps<br />
and directions], Keck Center is Building 28 on the Campus Map [https://www.chapman.edu/about/_files/maps-and-directions/current-maps/campus-map.pdf <br />
Campus map]<br />
<br />
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<br />
<br />
=== Friday, Feb 21st, 2020, noon - 1 pm in Keck 370, refreshments at 11:45 am (same room) ===<br />
<br />
==== ''Speaker:'' '''Christian Williams, University of California at Riverside''' ====<br />
<br />
''Title:'' '''Predicate Calculus for Algebraic Theories'''<br />
<br />
''Abstract:'' There is a notion of predicate for algebraic theories, which admits a calculus of both logical and algebraic operations. We thereby extend equational logic by first-order logic, and provide a natural type theory for algebraic structures.<br />
<br />
We demonstrate the idea with the theory of monoids, and derive the example predicate "prime". This and many algebraic examples are only useful when they are mapped from a theory into actual models. There is much to be done in this direction. However, the driving motivation of this work is the application to programming languages: we focus on applying the idea to a more general notion of theory with variable binding.<br />
<br />
The construction is given in the topos of presheaves on a theory T: a "predicate" is a sieve on an object t of T, which corresponds to a subfunctor of the representable T(-,t). For each type t, these predicates form a Heyting algebra, providing the constructors of intuitionistic logic. The operations of T can be lifted to act on predicates, and we construct a model Pred(T): T -->HeyAlg. The correspondence between the operations of T and those in the image of Pred(T) gives that the former are "polymorphic" with respect to the types of the latter. This process can be understood as providing the theory T with a polymorphic type system.<br />
<br />
The original motivation of this work is a logic for concurrency known as Namespace Logic. This applies to the reflective higher-order pi calculus, which is the language of the distributed computing platform RChain. We demonstrate the above framework by constructing namespace logic. This gives a glimpse into a large field of potential application.<br />
<br />
[http://math.chapman.edu/~jipsen/seminarposters/Christian_Williams_pcat_2020-02-21.pdf Slides from the talk]<br />
<br />
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<br />
=== Wednesday, Feb 19th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Simon Cho, University of Michigan''' ====<br />
''Title:'' '''A categorical perspective on persistent and magnitude homology'''<br />
<br />
''Abstract:'' We define and explain both persistent homology and magnitude homology, and their respective roles in applications (in both pure and applied settings). We will exhibit how both arise as a "singular complex" of a metric space in essentially the same way, but for different values of a parameter.<br />
<br />
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<br />
=== Wednesday, Feb 12th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Stephon Alexander, Brown University, Rhode Island''' ====<br />
''Title:'' '''The Quantum Cosmological Constant'''<br />
<br />
''Abstract:'' The mysteries surrounding the Cosmological Constant presides at the interface of quantum mechanics and gravity. In this seminar,<br />
I will provide a pedagogical discussion of the many faces of the cosmological constant problem and discuss some current research that<br />
paves new directions that invites us to rethink the quantum nature of vacuum energy.<br />
<br />
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<br />
=== Tuesday, Jan 14th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Pedram Roushan, Google Inc., Santa Barbara, CA''' ====<br />
''Title:'' '''Quantum supremacy using a programmable superconducting processor'''<br />
<br />
''Abstract:'' The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor1. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 2^53 (about 10^16). Measurements from repeated experiments sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 seconds to sample one instance of a quantum circuit a million times—our benchmarks currently indicate that the equivalent task for a state-of-the-art classical supercomputer would take approximately 10,000 years. This dramatic increase in speed compared to all known classical algorithms is an experimental realization of quantum supremacy for this specific computational task, heralding a much-anticipated computing paradigm. If time permits, I will present some of our more recent measurements. <br />
<br />
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<br />
== Fall 2019 ==<br />
<br />
The seminar talks are held in '''Keck Center for Science and Engineering, KC 370''' (Center St. Orange, CA 92866, intersection of Center St. And Sycamore St.), '''usually on Wednesday at 4 pm'''.<br />
Sometimes there will be a change of time or venue and the announcement will reflect this change.<br />
<br />
See [http://www.chapman.edu/about/maps-directions/index.aspx Maps<br />
and directions], Keck Center is Building 28 on the Campus Map [https://www.chapman.edu/about/_files/maps-and-directions/current-maps/campus-map.pdf <br />
Campus map]<br />
<br />
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<br />
=== Thursday, Dec 12th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Alí Guzmán Adán, Universiteit Gent, Belgium''' ====<br />
''Title:'' '''Pizzetti and Cauchy formulae for higher dimensional surfaces: a<br />
distributional approach'''<br />
<br />
''Abstract:'' In this talk, we study Pizzetti-type formulas for Stiefel<br />
manifolds and Cauchy-type formulas for the tangential Dirac operator<br />
from a distributional perspective. First, we illustrate a general<br />
distributional method for integration over manifolds in R^m defined by<br />
means of k equations. We apply this method to derive an alternative<br />
proof of the Pizzetti formulae for the real Stiefel manifolds<br />
SO(m)/SO(m-k). Besides, a distributional interpretation of invariant<br />
oriented integration is provided. In particular, we obtain a<br />
distributional Cauchy theorem for the tangential Dirac operator on an<br />
embedded (m-k)-dimensional smooth surface.<br />
<br />
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<br />
=== Wednesday, Dec 11th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Arjendu K Pattanayak, Physics and Astronomy, Carleton College, Northfield, Minnesota''' ====<br />
''Title:'' '''Quantum entanglement and tunneling oscillations in a (few) many-body nonlinear spin system'''<br />
<br />
''Abstract:'' Quantum tunnelling permits recoherence or refocusing in real or phase space after the initial quantum state has seemingly delocalized, exhibiting so-called classically forbidden dynamics. For a nonlinearly interacting many-body spin system this interim state can be an entangled state. We report on recent results from investigations into this phenomenon for initially spin coherent pure states in the paradigmatic kicked top (vale Haake) system. This has a mixed regualar and chaotic phase space in the classical limit and exhibits the entanglement tunneling described above, including coherent dynamics between phase-space stability islands; here the interim state is maximally entangled. We map the dependence on various parameters including nonlinear spin and number of spins involved (focusing mostly on the remarkable special case N=4) using a metric that attempts to quantify the quality and rate of tunnelling. The calculations of tunneling rates using eigenvalues and eigenstates of the time evolution operator as a function of initial condition compared to classical space structures demonstrates several nontrivial ways in which quantum behavior transitions to classical as the size of the system grows.<br />
<br />
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<br />
=== Wednesday, Dec 4th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Raphael Drumond, Universidade Federal de Minas Gerais, Brazil''' ====<br />
''Title:'' '''The basics of Quantum Darwinism (and its relationship with non-Markovianity)'''<br />
<br />
''Abstract:'' Some aspects of physical systems described by quantum <br />
mechanics, most notably the possibility of violating a Bell inequality, <br />
suggests (to some) or unavoidably implies (to others) that certain <br />
properties of microscopic systems, like the precise values of position <br />
and momentum of a fundamental particle, do not have an objective <br />
reality. This strongly contrasts with the objectivity of properties of <br />
everyday macroscopic systems like the (rough estimate of) position and <br />
momentum of a baseball. Now, how can this objectivity of the <br />
macroscopic world emerge from a theory where, apparently, not all <br />
aspects of physical systems are objective? The notion of quantum <br />
Darwinism, put forward and popularized by Wojciech Zurek, is a path in <br />
that direction. In this talk I will discuss the main ideas behind <br />
quantum Darwinism, explore it in some simple models, and briefly discuss <br />
its relationship (or the lack of it) with the notion of non-Markovianity <br />
of quantum dynamical systems.<br />
<br />
<br />
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<br />
=== Thursday, Nov 21th, 2019, 12:30 - 1:30 pm in Keck 370, refreshments from 12:15 (same room) ===<br />
<br />
==== ''Speaker:'' '''Sandu Popescu, University of Bristol, UK''' ====<br />
''Title:'' '''Exploring the limits of no-backward-in-time signaling'''<br />
<br />
''Abstract:'' One of the most routine observations that we make about our world is that we cannot signal backwards in time. So ubiquitous is this understanding that it is often taken as one of the basic laws of Nature. At first glance, this remark seems straightforward. However, as I will show, in probabilistic theories such as quantum mechanics, the consequences of such an assertion are far more involved. In fact, we will see that there is a surprising amount of liberty: some theories even allow the future to affect the past, nevertheless without signaling backwards in time.<br />
<br />
<br />
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<br />
=== Friday, Nov 8th, 2019, 3 - 4 pm in Keck 171, refreshments from 2:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Fredrik Dahlqvist, University College London, UK''' ====<br />
<br />
''Title:'' '''A probabilistic approach to floating point arithmetic'''<br />
<br />
''Abstract:'' Finite-precision floating point arithmetic introduces rounding errors which are traditionally bounded using a worst-case analysis. However, worst-case analysis might be overly conservative because worst-case errors can be extremely rare events in practice. Here we develop a probabilistic model of rounding errors with which it becomes possible to quantify the likelihood that the rounding error of an algorithm lies within a given interval. <br />
<br />
Given an input distribution, the model requires the distribution of rounding errors. We show how to exactly compute this distribution for low precision arithmetic. For high precision arithmetic we derive a simple but surprisingly useful approximation. The model is then entirely compositional: given a numerical program written in a simple imperative programing language we can recursively compute the distribution of rounding errors at each step and propagate it through each program instruction. This is done by applying a formalism originaly developed by Kozen to understand the semantics of probabilistic programs, for example how probability distributions gets transformed by assignments or "if then else" statements.<br />
<br />
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<br />
=== Wednesday, Nov 6th, 2019, 4 - 5 pm in Keck 370, refreshments from 3:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Jacques Pienaar, International Institute of Physics in Natal, Brazil''' ====<br />
<br />
''Title:'' '''The new question in quantum foundations: what is causality?'''<br />
<br />
''Abstract:'' Work in quantum foundations has tended to concentrate on Bell's Theorem, <br />
but recently a particular aspect of that theorem has taken on a life of <br />
its own: the question of what "causality" means in quantum mechanics, <br />
and how to model it. This movement has been driven in large part by <br />
recent advances in causal modeling in the statistical and Artificial <br />
Intelligence communities, which have had a heavy influence on quantum <br />
causal modeling. These "classical" approaches tend to define causality <br />
as a probabilistic and action-centered concept, which fits well with <br />
modern information-theoretic treatments of quantum mechanics. However, <br />
the classical approaches also tend to emphasize notions of underlying <br />
determinism and objective mechanisms that do not sit so well in the <br />
quantum context. In this talk I will step back from most of the <br />
technical jargon and try to get to the heart of some of the conceptual <br />
issues involved in "quantizing" the concept of causality, critically <br />
reviewing some key findings, pointing out potential inconsistencies and <br />
outlining possible directions for further inquiry into this fascinating <br />
problem.<br />
<br />
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<br />
=== Friday, October 18th, 2019, 12 - 1 pm in Keck 370, refreshments from 11:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Prof. Lev Vaidman, Alex Maguy-Glass Chair in Physics of Complex Systems, Tel Aviv University, Israel''' ====<br />
<br />
''Title:'' '''The past of a quantum particle'''<br />
<br />
''Abstract:'' Textbooks of quantum mechanics lack the concept of the past of quantum systems. Few years ago I proposed to define the past of a quantum particle according to the trace it leaves. While in many cases this definition provides a reasonable description, for a nested Mach-Zehnder interferometer it leads to a picture seemingly contradicting common sense: the particle leaves a trace in a place through which it could not pass. I will discuss recent theoretical and experimental studies of this controversial issue.<br />
<br />
<br />
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----<br />
<br />
=== Friday, October 11th, 2019, 1 - 2 pm in Keck 370, refreshments from 12:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Prof. Thomas Curtright, University of Miami''' ====<br />
<br />
''Title:'' '''Massive Dual Gravity Revisited'''<br />
<br />
''Abstract:'' I will describe a highly speculative model of gravity as a massive,<br />
pure spin 2 field, which is "dual" to the usual description in terms of<br />
a spacetime metric tensor.<br />
<br />
In the dual description, for weak fields, the metric emerges as the<br />
field strength of an underlying fundamental field. More generally, if<br />
the gravitational field is not weak, the metric emerges as a nonlinear<br />
mixture involving the energy momentum tensor.<br />
<br />
<br />
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----<br />
<br />
=== Wednesday, October 9th, 2019, 4 - 5 pm in Keck 370, refreshments from 3:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Alain Hénaut, Institut de Mathématiques de Bordeaux, Université de Bordeaux, France''' ====<br />
<br />
''Title:'' '''On planar web geometry'''<br />
<br />
''Abstract:'' Web geometry deals with foliations in general position. In the planar case and the complex setting, a $d$-web is given by the generic family of integral curves of an analytic or an algebraic differential equation $F(x,y,y')=0$ with $y'$-degree $d$. Invariants of these configurations as abelian relations (related to Abel's addition theorem), Lie symmetries or Godbillon-Vey sequences are investigated. This viewpoint enlarges the qualitative study of differential equations and their moduli. In the nonsingular case and through the singularities, Cartan-Spencer and meromorphic connections methods will be used. Basic examples will be given from different domains including classic algebraic geometry and WDVV-equations. Standard results and open problems will be mentioned. Illustration of the interplay between differential and algebraic geometry, new results will be presented. <br />
<br />
<br />
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----<br />
<br />
=== Thursday, September 5th, 2019, 4 - 5 pm in Keck 171, refreshments from 3:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Nicole Yunger Halpern, Harvard-Smithsonian ITAMP (Institute for Theoretical Atomic, Molecular, and Optical Physics) Harvard University Department of Physics''' ====<br />
<br />
''Title:'' '''Entropic uncertainty relations for quantum-information scrambling'''<br />
<br />
''Abstract:'' How violently do two quantum operators disagree? Different subfields of physics feature different notions of incompatibility: (i) In quantum information theory, uncertainty relations are cast in terms of entropies. These entropic uncertainty relations constrain measurement outcomes. (ii) Condensed matter and high-energy physics feature interacting quantum many-body systems, such as spin chains. A local perturbation, such as a Pauli operator on one side of a chain, spreads through many-body entanglement. The perturbation comes to overlap, and to disagree, with probes localized on the opposite side of the system. This disagreement signals that quantum information about the perturbation has scrambled, or become hidden in highly nonlocal correlations. I will unite these two notions of quantum operator disagreement, presenting an entropic uncertainty relation for quantum-information scrambling. The entropies are of distributions over weak and strong measurements’ possible outcomes. The uncertainty bound strengthens when a spin chain scrambles in numerical simulations. Hence the subfields—quantum information, condensed matter, and high-energy physics—can agree about when quantum operations disagree. Our relation can be tested experimentally with superconducting qubits, trapped ions, and quantum dots.<br />
<br />
NYH, Bartolotta, and Pollack, Comms. Phys. 2, 92 (2019). https://www.nature.com/articles/s42005-019-0179-8<br />
<br />
<br />
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<br />
=== Monday, August 26, 2019, 7 - 8:30 pm, in Argyros Forum, Room 209 A&B, networking from 6:15 to 7pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Frederick Eberhardt, Professor of Philosophy in the Division of the Humanities and Social Sciences at the California Institute of Technology''' ====<br />
<br />
''Title:'' '''Computing Causal Relations at Scale or Causality: From Aristotle through Computing to Zebrafish'''<br />
<br />
''Abstract:'' What causes what? How do we untangle the “why” behind processes that regulate the brain, the climate or the economy? If “Correlation does not imply causation" is the standard mantra in science, how can we ever discover causal relationships behind the data? Will it ever be possible for intelligent AI to make its own deductions and predictions? In recent years researchers have developed mathematical techniques that give us the power to infer the underlying “why” behind scientific data. What’s more, we’ve learned that we can discover these causes without performing experiments. Starting with a little practical example with lightbulbs that can be worked out by hand we will see how the problem scales as the number of variables increases. To compute the neural connections in a zebrafish brain, high performance computing is essential.<br />
<br />
''Bio:'' Frederick Eberhardt is Professor of Philosophy in the Division of the Humanities and Social Sciences at the California Institute of Technology. Before coming to Caltech he was Assistant Professor in the Philosophy-Neuroscience-Psychology (PNP) program and the Department of Philosophy at Washington University in St. Louis and a postdoc at the Institute of Cognitive and Brain Sciences at the University of California, Berkeley. As an undergraduate he attended the London School of Economics for a Bachelor in Philosophy & Mathematics. He received his PhD in philosophy from Carnegie Mellon University, where he also completed a Masters in Machine Learning.<br />
<br />
His research interests lie at the intersection of philosophy of science, machine learning and statistics. He is particularly interested in the development of methods for causal discovery from statistical data.<br />
<br />
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<br />
<br />
== Previous Seminar talks ==<br />
<br />
* [[MPC Seminar 2019]]<br />
<br />
* [[MPC Seminar 2018]]<br />
<br />
* [[MathCS Seminar 2017]]<br />
<br />
* [[MathCS Seminar 2016]]<br />
<br />
* [[MathCS Seminar 2015]]<br />
<br />
* [[MathCS Seminar 2014]]<br />
<br />
* [[MathCS Seminar 2013]]<br />
<br />
* [[MathCS Seminar 2012]]<br />
<br />
* [[MathCS Seminar 2011]]<br />
<br />
* [[MathCS Seminar 2010]]<br />
<br />
* [[MathCS Seminar 2009]]<br />
<br />
* [[MathCS Seminar 2008]]<br />
<br />
* [[MathCS Seminar 2007]]<br />
<br />
* [[MathCS Seminar 2006]]<br />
<br />
* [[MathCS Seminar 2005]]<br />
<br />
* [[MathCS Seminar 2004]]<br />
<br />
* [[MathCS Seminar 2003]]<br />
<br />
* [[MathCS Seminar 2002]]</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=MPC_Seminar&diff=23MPC Seminar2021-05-02T18:17:07Z<p>Jipsen: </p>
<hr />
<div>This is the homepage of the Chapman University '''Mathematics, Physics, and Computation Seminars'''<br />
([[MPC Seminar]])<br />
<br />
''Seminar Organizers:'' Roman Buniy and Peter Jipsen<br />
<br />
<br />
== Spring 2021 ==<br />
<br />
The MPC seminar is held via Zoom for now. The Zoom address will be sent in the email announcements (email jipsen@chapman.edu if you would like to have your email address added to the mailing list).<br />
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<br />
<br />
=== Monday, May 3rd, 2021, 1 - 2 pm on Zoom ===<br />
<br />
==== ''Speaker:'' '''Simon Henry, University of Ottawa''' ====<br />
<br />
''Title:'' '''Localic C*-algebras and the Geometric Bohr topos'''<br />
<br />
''Abstract:'' The Bohr topos is a space attached to a C*-algebra A that has been introduced in the hope of producing a new point of view on the mathematics of Quantum mechanics. It is essentially the "space of commutative sub-C*-algebra of A". But its original construction had two problems: (1) it had "the wrong topology" and (2) it was a "non-geometric" construction, i.e. when applied to continuous families of C*-algebras, it wasn't compatible with certain change-of-base functors. In this talk I'll explain how the theory of localic C*-algebras and some classical idea from "geometric logic" allows to give a new version of this construction that solves both of these problems.<br />
<br />
''Link to paper:'' [https://arxiv.org/pdf/1502.01896.pdf arxiv.org/pdf/1502.01896.pdf]<br />
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<br />
=== Thursday, Jan 21st, 2021, 4 - 5 pm on Zoom ===<br />
<br />
==== ''Speaker:'' '''Mike Campbell, Eureka (SAP), joint work with Vernon Smith (Chapman University)''' ====<br />
<br />
''Title:'' '''An Elementary Humanomics Approach to Boundedly Rational Quadratic Models'''<br />
<br />
''Video of talk:'' [https://youtu.be/F74RlCAjC_A YouTube] ''Slides:'' [http://math.chapman.edu/~jipsen/seminarposters/MikeCampbell2021HumanomicsApproachBRQuadratic.pdf pdf]<br />
<br />
''Abstract:'' We take a refreshing new look at boundedly rational quadratic models in economics using some elementary modeling of the principles put forward in the book Humanomics by Vernon L. Smith and Bart J. Wilson. A simple model is introduced built on the fundamental Humanomics principles of gratitude/resentment felt and the corresponding action responses of reward/punishment in the form of higher/lower payoff transfers. There are two timescales: one for strictly self-interested action, as in economic equilibrium, and another governed by feelings of gratitude/resentment. One of three timescale scenarios is investigated: one where gratitude/resentment changes much more slowly than economic equilibrium ("quenched model"). Another model, in which economic equilibrium occurs over a much slower time than gratitude/resent evolution ("annealed model") is set up, but not investigated. The quenched model with homogeneous interactions turns out to be a non-frustrated spin-glass model. A two-agent quenched model with heterogeneous aligning (ferromagnetic) interactions is analyzed and yields new insights into the critical quenched probability p (1-p) that represents the empirical frequency of opportunity for agent i to take action for the benefit (hurt) of other that invokes mutual gratitude (resentment). A critical quenched probability p*i, i=1,2, exists for each agent. When p < p*i, agent i will choose action in their self-interest. When p > p*i, agent i will take action sensitive to their interpersonal feelings of gratitude/resentment and thus reward/punish the initiating benefit/hurt. We find that the p*i are greater than one-half, which implies agents are averse to resentful behavior and punishment. This was not built into the model, but is a result of its properties, and consistent with Axiom 4 in Humanomics about the asymmetry of gratitude and resentment. Furthermore, the agent who receives less payoff is more averse to resentful behavior; i.e., has a higher critical quenched probability. For this particular model, the Nash equilibrium has no predictive power of Humanomics properties since the rewards are the same for self-interested behavior, resentful behavior, and gratitude behavior. Accordingly, we see that the boundedly rational Gibbs equilibrium does indeed lead to richer properties.<br />
<br />
''Link to paper:'' [https://digitalcommons.chapman.edu/cgi/viewcontent.cgi?article=1330&context=esi_working_papers Chapman Digital Commons]<br />
<br />
== Spring 2020 ==<br />
<br />
The seminar talks are held in '''Keck Center for Science and Engineering, KC 370''' (Center St. Orange, CA 92866, intersection of Center St. And Sycamore St.), '''usually on Wednesday at 4 pm'''.<br />
Sometimes there will be a change of time or venue and the announcement will reflect this change.<br />
<br />
See [http://www.chapman.edu/about/maps-directions/index.aspx Maps<br />
and directions], Keck Center is Building 28 on the Campus Map [https://www.chapman.edu/about/_files/maps-and-directions/current-maps/campus-map.pdf <br />
Campus map]<br />
<br />
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<br />
=== Friday, Feb 21st, 2020, noon - 1 pm in Keck 370, refreshments at 11:45 am (same room) ===<br />
<br />
==== ''Speaker:'' '''Christian Williams, University of California at Riverside''' ====<br />
<br />
''Title:'' '''Predicate Calculus for Algebraic Theories'''<br />
<br />
''Abstract:'' There is a notion of predicate for algebraic theories, which admits a calculus of both logical and algebraic operations. We thereby extend equational logic by first-order logic, and provide a natural type theory for algebraic structures.<br />
<br />
We demonstrate the idea with the theory of monoids, and derive the example predicate "prime". This and many algebraic examples are only useful when they are mapped from a theory into actual models. There is much to be done in this direction. However, the driving motivation of this work is the application to programming languages: we focus on applying the idea to a more general notion of theory with variable binding.<br />
<br />
The construction is given in the topos of presheaves on a theory T: a "predicate" is a sieve on an object t of T, which corresponds to a subfunctor of the representable T(-,t). For each type t, these predicates form a Heyting algebra, providing the constructors of intuitionistic logic. The operations of T can be lifted to act on predicates, and we construct a model Pred(T): T -->HeyAlg. The correspondence between the operations of T and those in the image of Pred(T) gives that the former are "polymorphic" with respect to the types of the latter. This process can be understood as providing the theory T with a polymorphic type system.<br />
<br />
The original motivation of this work is a logic for concurrency known as Namespace Logic. This applies to the reflective higher-order pi calculus, which is the language of the distributed computing platform RChain. We demonstrate the above framework by constructing namespace logic. This gives a glimpse into a large field of potential application.<br />
<br />
[http://math.chapman.edu/~jipsen/seminarposters/Christian_Williams_pcat_2020-02-21.pdf Slides from the talk]<br />
<br />
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=== Wednesday, Feb 19th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Simon Cho, University of Michigan''' ====<br />
''Title:'' '''A categorical perspective on persistent and magnitude homology'''<br />
<br />
''Abstract:'' We define and explain both persistent homology and magnitude homology, and their respective roles in applications (in both pure and applied settings). We will exhibit how both arise as a "singular complex" of a metric space in essentially the same way, but for different values of a parameter.<br />
<br />
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<br />
=== Wednesday, Feb 12th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Stephon Alexander, Brown University, Rhode Island''' ====<br />
''Title:'' '''The Quantum Cosmological Constant'''<br />
<br />
''Abstract:'' The mysteries surrounding the Cosmological Constant presides at the interface of quantum mechanics and gravity. In this seminar,<br />
I will provide a pedagogical discussion of the many faces of the cosmological constant problem and discuss some current research that<br />
paves new directions that invites us to rethink the quantum nature of vacuum energy.<br />
<br />
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<br />
=== Tuesday, Jan 14th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Pedram Roushan, Google Inc., Santa Barbara, CA''' ====<br />
''Title:'' '''Quantum supremacy using a programmable superconducting processor'''<br />
<br />
''Abstract:'' The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor1. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 2^53 (about 10^16). Measurements from repeated experiments sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 seconds to sample one instance of a quantum circuit a million times—our benchmarks currently indicate that the equivalent task for a state-of-the-art classical supercomputer would take approximately 10,000 years. This dramatic increase in speed compared to all known classical algorithms is an experimental realization of quantum supremacy for this specific computational task, heralding a much-anticipated computing paradigm. If time permits, I will present some of our more recent measurements. <br />
<br />
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<br />
== Fall 2019 ==<br />
<br />
The seminar talks are held in '''Keck Center for Science and Engineering, KC 370''' (Center St. Orange, CA 92866, intersection of Center St. And Sycamore St.), '''usually on Wednesday at 4 pm'''.<br />
Sometimes there will be a change of time or venue and the announcement will reflect this change.<br />
<br />
See [http://www.chapman.edu/about/maps-directions/index.aspx Maps<br />
and directions], Keck Center is Building 28 on the Campus Map [https://www.chapman.edu/about/_files/maps-and-directions/current-maps/campus-map.pdf <br />
Campus map]<br />
<br />
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<br />
=== Thursday, Dec 12th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Alí Guzmán Adán, Universiteit Gent, Belgium''' ====<br />
''Title:'' '''Pizzetti and Cauchy formulae for higher dimensional surfaces: a<br />
distributional approach'''<br />
<br />
''Abstract:'' In this talk, we study Pizzetti-type formulas for Stiefel<br />
manifolds and Cauchy-type formulas for the tangential Dirac operator<br />
from a distributional perspective. First, we illustrate a general<br />
distributional method for integration over manifolds in R^m defined by<br />
means of k equations. We apply this method to derive an alternative<br />
proof of the Pizzetti formulae for the real Stiefel manifolds<br />
SO(m)/SO(m-k). Besides, a distributional interpretation of invariant<br />
oriented integration is provided. In particular, we obtain a<br />
distributional Cauchy theorem for the tangential Dirac operator on an<br />
embedded (m-k)-dimensional smooth surface.<br />
<br />
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<br />
=== Wednesday, Dec 11th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Arjendu K Pattanayak, Physics and Astronomy, Carleton College, Northfield, Minnesota''' ====<br />
''Title:'' '''Quantum entanglement and tunneling oscillations in a (few) many-body nonlinear spin system'''<br />
<br />
''Abstract:'' Quantum tunnelling permits recoherence or refocusing in real or phase space after the initial quantum state has seemingly delocalized, exhibiting so-called classically forbidden dynamics. For a nonlinearly interacting many-body spin system this interim state can be an entangled state. We report on recent results from investigations into this phenomenon for initially spin coherent pure states in the paradigmatic kicked top (vale Haake) system. This has a mixed regualar and chaotic phase space in the classical limit and exhibits the entanglement tunneling described above, including coherent dynamics between phase-space stability islands; here the interim state is maximally entangled. We map the dependence on various parameters including nonlinear spin and number of spins involved (focusing mostly on the remarkable special case N=4) using a metric that attempts to quantify the quality and rate of tunnelling. The calculations of tunneling rates using eigenvalues and eigenstates of the time evolution operator as a function of initial condition compared to classical space structures demonstrates several nontrivial ways in which quantum behavior transitions to classical as the size of the system grows.<br />
<br />
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<br />
=== Wednesday, Dec 4th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Raphael Drumond, Universidade Federal de Minas Gerais, Brazil''' ====<br />
''Title:'' '''The basics of Quantum Darwinism (and its relationship with non-Markovianity)'''<br />
<br />
''Abstract:'' Some aspects of physical systems described by quantum <br />
mechanics, most notably the possibility of violating a Bell inequality, <br />
suggests (to some) or unavoidably implies (to others) that certain <br />
properties of microscopic systems, like the precise values of position <br />
and momentum of a fundamental particle, do not have an objective <br />
reality. This strongly contrasts with the objectivity of properties of <br />
everyday macroscopic systems like the (rough estimate of) position and <br />
momentum of a baseball. Now, how can this objectivity of the <br />
macroscopic world emerge from a theory where, apparently, not all <br />
aspects of physical systems are objective? The notion of quantum <br />
Darwinism, put forward and popularized by Wojciech Zurek, is a path in <br />
that direction. In this talk I will discuss the main ideas behind <br />
quantum Darwinism, explore it in some simple models, and briefly discuss <br />
its relationship (or the lack of it) with the notion of non-Markovianity <br />
of quantum dynamical systems.<br />
<br />
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<br />
=== Thursday, Nov 21th, 2019, 12:30 - 1:30 pm in Keck 370, refreshments from 12:15 (same room) ===<br />
<br />
==== ''Speaker:'' '''Sandu Popescu, University of Bristol, UK''' ====<br />
''Title:'' '''Exploring the limits of no-backward-in-time signaling'''<br />
<br />
''Abstract:'' One of the most routine observations that we make about our world is that we cannot signal backwards in time. So ubiquitous is this understanding that it is often taken as one of the basic laws of Nature. At first glance, this remark seems straightforward. However, as I will show, in probabilistic theories such as quantum mechanics, the consequences of such an assertion are far more involved. In fact, we will see that there is a surprising amount of liberty: some theories even allow the future to affect the past, nevertheless without signaling backwards in time.<br />
<br />
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=== Friday, Nov 8th, 2019, 3 - 4 pm in Keck 171, refreshments from 2:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Fredrik Dahlqvist, University College London, UK''' ====<br />
<br />
''Title:'' '''A probabilistic approach to floating point arithmetic'''<br />
<br />
''Abstract:'' Finite-precision floating point arithmetic introduces rounding errors which are traditionally bounded using a worst-case analysis. However, worst-case analysis might be overly conservative because worst-case errors can be extremely rare events in practice. Here we develop a probabilistic model of rounding errors with which it becomes possible to quantify the likelihood that the rounding error of an algorithm lies within a given interval. <br />
<br />
Given an input distribution, the model requires the distribution of rounding errors. We show how to exactly compute this distribution for low precision arithmetic. For high precision arithmetic we derive a simple but surprisingly useful approximation. The model is then entirely compositional: given a numerical program written in a simple imperative programing language we can recursively compute the distribution of rounding errors at each step and propagate it through each program instruction. This is done by applying a formalism originaly developed by Kozen to understand the semantics of probabilistic programs, for example how probability distributions gets transformed by assignments or "if then else" statements.<br />
<br />
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<br />
=== Wednesday, Nov 6th, 2019, 4 - 5 pm in Keck 370, refreshments from 3:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Jacques Pienaar, International Institute of Physics in Natal, Brazil''' ====<br />
<br />
''Title:'' '''The new question in quantum foundations: what is causality?'''<br />
<br />
''Abstract:'' Work in quantum foundations has tended to concentrate on Bell's Theorem, <br />
but recently a particular aspect of that theorem has taken on a life of <br />
its own: the question of what "causality" means in quantum mechanics, <br />
and how to model it. This movement has been driven in large part by <br />
recent advances in causal modeling in the statistical and Artificial <br />
Intelligence communities, which have had a heavy influence on quantum <br />
causal modeling. These "classical" approaches tend to define causality <br />
as a probabilistic and action-centered concept, which fits well with <br />
modern information-theoretic treatments of quantum mechanics. However, <br />
the classical approaches also tend to emphasize notions of underlying <br />
determinism and objective mechanisms that do not sit so well in the <br />
quantum context. In this talk I will step back from most of the <br />
technical jargon and try to get to the heart of some of the conceptual <br />
issues involved in "quantizing" the concept of causality, critically <br />
reviewing some key findings, pointing out potential inconsistencies and <br />
outlining possible directions for further inquiry into this fascinating <br />
problem.<br />
<br />
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<br />
=== Friday, October 18th, 2019, 12 - 1 pm in Keck 370, refreshments from 11:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Prof. Lev Vaidman, Alex Maguy-Glass Chair in Physics of Complex Systems, Tel Aviv University, Israel''' ====<br />
<br />
''Title:'' '''The past of a quantum particle'''<br />
<br />
''Abstract:'' Textbooks of quantum mechanics lack the concept of the past of quantum systems. Few years ago I proposed to define the past of a quantum particle according to the trace it leaves. While in many cases this definition provides a reasonable description, for a nested Mach-Zehnder interferometer it leads to a picture seemingly contradicting common sense: the particle leaves a trace in a place through which it could not pass. I will discuss recent theoretical and experimental studies of this controversial issue.<br />
<br />
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=== Friday, October 11th, 2019, 1 - 2 pm in Keck 370, refreshments from 12:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Prof. Thomas Curtright, University of Miami''' ====<br />
<br />
''Title:'' '''Massive Dual Gravity Revisited'''<br />
<br />
''Abstract:'' I will describe a highly speculative model of gravity as a massive,<br />
pure spin 2 field, which is "dual" to the usual description in terms of<br />
a spacetime metric tensor.<br />
<br />
In the dual description, for weak fields, the metric emerges as the<br />
field strength of an underlying fundamental field. More generally, if<br />
the gravitational field is not weak, the metric emerges as a nonlinear<br />
mixture involving the energy momentum tensor.<br />
<br />
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<br />
=== Wednesday, October 9th, 2019, 4 - 5 pm in Keck 370, refreshments from 3:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Alain Hénaut, Institut de Mathématiques de Bordeaux, Université de Bordeaux, France''' ====<br />
<br />
''Title:'' '''On planar web geometry'''<br />
<br />
''Abstract:'' Web geometry deals with foliations in general position. In the planar case and the complex setting, a $d$-web is given by the generic family of integral curves of an analytic or an algebraic differential equation $F(x,y,y')=0$ with $y'$-degree $d$. Invariants of these configurations as abelian relations (related to Abel's addition theorem), Lie symmetries or Godbillon-Vey sequences are investigated. This viewpoint enlarges the qualitative study of differential equations and their moduli. In the nonsingular case and through the singularities, Cartan-Spencer and meromorphic connections methods will be used. Basic examples will be given from different domains including classic algebraic geometry and WDVV-equations. Standard results and open problems will be mentioned. Illustration of the interplay between differential and algebraic geometry, new results will be presented. <br />
<br />
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<br />
=== Thursday, September 5th, 2019, 4 - 5 pm in Keck 171, refreshments from 3:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Nicole Yunger Halpern, Harvard-Smithsonian ITAMP (Institute for Theoretical Atomic, Molecular, and Optical Physics) Harvard University Department of Physics''' ====<br />
<br />
''Title:'' '''Entropic uncertainty relations for quantum-information scrambling'''<br />
<br />
''Abstract:'' How violently do two quantum operators disagree? Different subfields of physics feature different notions of incompatibility: (i) In quantum information theory, uncertainty relations are cast in terms of entropies. These entropic uncertainty relations constrain measurement outcomes. (ii) Condensed matter and high-energy physics feature interacting quantum many-body systems, such as spin chains. A local perturbation, such as a Pauli operator on one side of a chain, spreads through many-body entanglement. The perturbation comes to overlap, and to disagree, with probes localized on the opposite side of the system. This disagreement signals that quantum information about the perturbation has scrambled, or become hidden in highly nonlocal correlations. I will unite these two notions of quantum operator disagreement, presenting an entropic uncertainty relation for quantum-information scrambling. The entropies are of distributions over weak and strong measurements’ possible outcomes. The uncertainty bound strengthens when a spin chain scrambles in numerical simulations. Hence the subfields—quantum information, condensed matter, and high-energy physics—can agree about when quantum operations disagree. Our relation can be tested experimentally with superconducting qubits, trapped ions, and quantum dots.<br />
<br />
NYH, Bartolotta, and Pollack, Comms. Phys. 2, 92 (2019). https://www.nature.com/articles/s42005-019-0179-8<br />
<br />
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<br />
=== Monday, August 26, 2019, 7 - 8:30 pm, in Argyros Forum, Room 209 A&B, networking from 6:15 to 7pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Frederick Eberhardt, Professor of Philosophy in the Division of the Humanities and Social Sciences at the California Institute of Technology''' ====<br />
<br />
''Title:'' '''Computing Causal Relations at Scale or Causality: From Aristotle through Computing to Zebrafish'''<br />
<br />
''Abstract:'' What causes what? How do we untangle the “why” behind processes that regulate the brain, the climate or the economy? If “Correlation does not imply causation" is the standard mantra in science, how can we ever discover causal relationships behind the data? Will it ever be possible for intelligent AI to make its own deductions and predictions? In recent years researchers have developed mathematical techniques that give us the power to infer the underlying “why” behind scientific data. What’s more, we’ve learned that we can discover these causes without performing experiments. Starting with a little practical example with lightbulbs that can be worked out by hand we will see how the problem scales as the number of variables increases. To compute the neural connections in a zebrafish brain, high performance computing is essential.<br />
<br />
''Bio:'' Frederick Eberhardt is Professor of Philosophy in the Division of the Humanities and Social Sciences at the California Institute of Technology. Before coming to Caltech he was Assistant Professor in the Philosophy-Neuroscience-Psychology (PNP) program and the Department of Philosophy at Washington University in St. Louis and a postdoc at the Institute of Cognitive and Brain Sciences at the University of California, Berkeley. As an undergraduate he attended the London School of Economics for a Bachelor in Philosophy & Mathematics. He received his PhD in philosophy from Carnegie Mellon University, where he also completed a Masters in Machine Learning.<br />
<br />
His research interests lie at the intersection of philosophy of science, machine learning and statistics. He is particularly interested in the development of methods for causal discovery from statistical data.<br />
<br />
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<br />
<br />
<br />
== Previous Seminar talks ==<br />
<br />
* [[MPC Seminar 2019]]<br />
<br />
* [[MPC Seminar 2018]]<br />
<br />
* [[MathCS Seminar 2017]]<br />
<br />
* [[MathCS Seminar 2016]]<br />
<br />
* [[MathCS Seminar 2015]]<br />
<br />
* [[MathCS Seminar 2014]]<br />
<br />
* [[MathCS Seminar 2013]]<br />
<br />
* [[MathCS Seminar 2012]]<br />
<br />
* [[MathCS Seminar 2011]]<br />
<br />
* [[MathCS Seminar 2010]]<br />
<br />
* [[MathCS Seminar 2009]]<br />
<br />
* [[MathCS Seminar 2008]]<br />
<br />
* [[MathCS Seminar 2007]]<br />
<br />
* [[MathCS Seminar 2006]]<br />
<br />
* [[MathCS Seminar 2005]]<br />
<br />
* [[MathCS Seminar 2004]]<br />
<br />
* [[MathCS Seminar 2003]]<br />
<br />
* [[MathCS Seminar 2002]]</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=MathCS_Seminar_2007&diff=22MathCS Seminar 20072021-02-22T19:05:47Z<p>Jipsen: Created page with "== Fall 2007 == The seminar talks are usually in Beckman Hall 207 (corner of [http://maps.google.com/maps?q=N+Glassell+St+%26+University+Dr,+Orange,+CA+92866,+USA&sa=X&oi=map..."</p>
<hr />
<div>== Fall 2007 ==<br />
<br />
The seminar talks are usually in Beckman Hall 207 (corner of [http://maps.google.com/maps?q=N+Glassell+St+%26+University+Dr,+Orange,+CA+92866,+USA&sa=X&oi=map&ct=title N. Glassell St and University Drive], Orange, CA 92866)<br />
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<br />
=== Thursday, November 15, 2007, 1:30-2:30 pm, BK 207 ===<br />
<br />
''Speaker:'' Dr. Adrian Vajiac, Chapman University<br />
<br />
''Title:'' Equivariant Localization in Mathematics and Physics II<br />
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<br />
=== Thursday, November 8, 2007, 1:30-2:30 pm, BK 207 ===<br />
<br />
''Speaker:'' Dr. Adrian Vajiac, Chapman University<br />
<br />
''Title:'' Equivariant Localization in Mathematics and Physics<br />
<br />
''Abstract:'' I will describe localization phenomena in mathematics and physics, especially recent applications of equivariant localization techniques and Weyl's integration formula in Topological Quantum Field Theories (TQFT). This is a summary of the talk I gave this summer at the "Recent Developments in Quantum Field Theory" conference held at the Max Plank Institute, Leipzig. I will conclude with a report on a work in progress regarding the relationship between equivariant localization and computational algebra techniques applied to 4 dimensional TQFTs.<br />
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<br />
=== Thursday, October 25, 2007, 1:30-2:30 pm, BK 207 ===<br />
<br />
''Speaker:'' Dr. Andrew Moshier, Chapman University<br />
<br />
''Title:'' Representations of Heyting Algebras in Bitopological Spaces II<br />
<br />
''Abstract:'' See below.<br />
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<br />
=== Thursday, October 18, 2007, 1:30-2:30 pm, BK 207 ===<br />
<br />
''Speaker:'' Dr. Andrew Moshier, Chapman University<br />
<br />
''Title:'' Representations of Heyting Algebras in Bitopological Spaces<br />
<br />
''Abstract:'' Heyting algebras formalize intuitionistic propositional logic in essentially the same way as Boolean algebras formalize classical propositional logic. While one can regard classical propositions as being characterized by their totality (in any world either "p" or "not p"), in contrast, tertium non datur fails in intuitionistic logic. This simple observation lead Kleene to investigate three-valued logic in which a proposition may be true, false or neither. As part of his investigation, Kleene showed that intuitionistic propositions can be translated into three-valued logic so that a proposition is intuitionistically valid if and only if its translate is valid in three-value logic. Of course, Kleene's program went much deeper, leading to many useful insights into the connection between intuitionistic mathematics and computation (recursion theory). But one important thing missing was a suitable topological representation theory. In this talk, we establish a representation theorem for Heyting algebras in bitopological spaces (spaces equipped with two topologies). In the course of developing this, we will see that the essentials of Kleene's ideas about three-valued logic resurface as a natural way to view a bitopological space. Time permitting we will also discuss connections to Priestley Duality via the work of Esakia.<br />
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<br />
=== Tuesday, October 2, 2007, 1:00-2:00 pm, BK 207 ===<br />
<br />
''Speaker:'' Prof. Gunduz Caginalp, University of Pittsburgh<br />
<br />
''Title:'' Toward a mathematical theory of financial market dynamics.<br />
<br />
''Abstract:'' Methodology for understanding the deterministic aspects of the dynamics of asset markets will be presented. These include differential and difference equations, optimization and statistical time-series methods. The integration of mathematical modeling with economics experiments will also be discussed.<br />
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<br />
=== Thursday, September 27, 2007, 1:30-2:30 pm, BK 207 ===<br />
<br />
''Speaker:'' Dr. Peter Jipsen, Chapman University<br />
<br />
''Title:'' The structure of the one-generated free domain semiring ''Abstract:'' In this talk we consider idempotent semirings with an additional unary operation d that has the properties of a domain operation. Concrete models of such algebras are e.g. reducts of relation algebras (with d(x)=(x;x^{-1})\cap id), as well as reducts of Kleene algebras with domain. Applications of these algebras to the semantic of various programming calculi have been considered by several researchers. Since both relation algebras and Kleene algebras have rich and complex (quasi)equational theories, we will only consider the simpler equational theory of idempotent semirings with domain.<br />
<br />
The aim of this talk is to give an explicit construction of the one-generated free domain semiring. In particular it is proved that the elements can be represented uniquely by finite antichains in the poset of finite strictly decreasing sequences of nonnegative integers. It is also shown that this domain semiring can be represented by sets of binary relations with union, composition and relational domain as operations.<br />
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<br />
=== Thursday, September 20, 2007, 1:30-2:30 pm ===<br />
<br />
''Speaker:'' Visiting Prof. Alberto Damiano, Chapman University<br />
<br />
''Title:'' Constructing Free Resolutions of Differential Operators - part II<br />
<br />
''Abstract:'' I will continue to talk about free resolutions for modules over the polynomial ring and define their cohomology modules. I will then shift to the non commutative case, and introduce the Weyl algebra, the Clifford algebra and the Exterior algebra. Gröbner basis type of algorithms have been studied recently for such algebras, allowing one to compute “effectively” syzygies and free resolutions. I will then show some examples of calculation using Singular, from which it will be clear that such methods are not really “efficient”, mostly because of the lack of a proper graded structure on such algebras.<br />
<br />
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<br />
=== Thursday, September 13, 2007, 1:30-2:30 pm ===<br />
<br />
''Speaker:'' Visiting Prof. Alberto Damiano, Chapman University<br />
<br />
''Title:'' Constructing Free Resolutions of Differential Operators - part I<br />
<br />
''Abstract:'' In this series of two talks, I will illustrate how to construct free resolutions associated to invariant differential operators. Since most of the examples of operators that have been studied within the framework of Algebraic Analysis are constant coefficient operators, this theory possesses mostly an algebraic flavor because an operator is viewed as a matrix with polynomial entries. In this first lecture, I will review some of the basic concepts of commutative and homological algebra such as:<br />
<br />
- Syzygies of ideals and modules over the polynomial ring<br />
<br />
- Complexes of free modules, free resolutions, “uniqueness” of the minimal free resolution of a graded module<br />
<br />
- Ext modules and cohomology<br />
<br />
Since all such objects can be effectively constructed thanks to the theory of Gröbner bases, I will show some examples of calculations using the software package CoCoA.<br />
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<br />
== Spring 2007 ==<br />
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<br />
=== Thursday, May 17, 2007, 12:30-1:50 pm ===<br />
<br />
''Speaker:'' Dr. Joanne Walters-Wayland<br />
<br />
''Title:'' Framing "Mel"<br />
<br />
''Abstract:'' Unfortunately I was unable to attend a recent conference in Baton Rouge honoring Professor Melvin Henriksen's 80th birthday. I had been allocated the opening slot for a short talk which was to be a tribute to Mel and the influence he has had, albeit mainly inadvertently, on frame theory. I decided to take the opportunity to present the talk I had intended to give in Baton Rouge when I was invited to speak at Chapman University. Here is my original ''Abstract:''<br />
<br />
"As a tribute to Mel Henriksen and, in thanks for, his ability to inspire and motivate, I would like to give a few snapshots of work he has done over the years, taken through a localic lens. Starting with work presented to the AMS in 1954 on finitely generated ideals, the "raison d'etre" of F-frames, P-frames etc, including his work on prime ideals (1965), quasi-F-covers (1987) and pretty bases (1991), and concluding with some results about cozero complemented spaces (2003)."<br />
<br />
I will give a brief introduction to Frame Theory at the beginning of the talk, and will conclude, if time permits, with a sketch of some of our (this is joint work with Rick Ball) recent results and problems in these areas.<br />
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<br />
=== Thursday, May 10, 2007, 12:30-1:50 pm ===<br />
<br />
''Speaker:'' Prof. Irene Sabatini<br />
<br />
''Title:'' An algebraic approach to Hermitian monogenic function<br />
<br />
''Abstract:'' In this talk we describe the algebraic analysis of the system of differential equations described by the Hermitian Dirac operator, which is a linear first order operator invariant with respect to the action of the unitary group. We show that it is possible to give explicit formulae for the first syzygies of the resolution associated to the system, and we study the removability of compact singularities. We will also discuss the quaternionic version of the hermitian system.<br />
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<br />
=== Thursday, May 3, 2007, 12:30-1:50 pm ===<br />
<br />
''Speaker:'' Dr. Andrew Moshier, Chapman University<br />
<br />
''Title:'' Generalizations of Topology with an Eye on Stone Duality<br />
<br />
''Abstract:'' One view of point-set topology is that it is the study of concrete representations of frames, i.e., complete lattices in which finite meet distributes over arbitrary join. The utility of this view comes into clear focus when we consider Stone Duality and its close relatives such as Priestley Duality. Recently, we have found a bitopological setting in which Stone and Priestley are unified, but this unification leaves open the question of how to relate topology (as the study of concrete representations of frames) to bitopology (as the study of concrete representations of what?). In this talk, we will make some preliminary steps toward a general approach to topological duality theorems in which topology and bitopology appear as special cases. We will look at possible further applications of this to so-called "quantum logic".<br />
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<br />
=== Thursday, April 26, 2007, 12:30-1:50 pm ===<br />
<br />
''Speaker:'' Dr. Ovidiu Munteanu, UCI<br />
<br />
''Title:'' Curvature invariants in submanifold geometry. New developments"<br />
<br />
''Abstract:'' In this talk we will discuss the structure at infinity of manifolds that admit a weighted Poincare inequality and have a Ricci curvature lower bound defined by the weight function. We will recall Li-Wang's fundamental results on the subject and discuss some new ideas.<br />
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<br />
=== Thursday, April 19, 2007 in BK 207, 12:30-1:50 pm ===<br />
<br />
''Speaker:'' Professor Fabrizio Colombo, Politecnico di Milano<br />
<br />
''Title:'' Identification of convolution memory kernels<br />
<br />
''Abstract:'' We investigate some abstract integrodifferential inverse problems that can be applied to the heat equation with memory, to the strongly damped wave equation with memory and to some other models.<br />
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<br />
=== Thursday, April 12, 2007, 12:30-1:50 pm ===<br />
<br />
''Speaker:'' Visiting Assistant Professor Nelia Charalambous, UCI<br />
<br />
''Title:'' The Yang-Mills heat equation on compact manifolds with boundary<br />
<br />
''Abstract:'' Gauge theory is the study of differential equations for fields over a principal bundle. The case of a principal bundle with a nonabelian group was first introduced by R.L. Mills and C.N. Yang ['54] in order to give a model of the weak and strong interactions in the nucleus of a particle. They wanted to mirror the invariance of physics under an infinite dimensional gauge group, also known as the principle of local invariance.<br />
<br />
In this talk we will consider a gauge-theoretic heat equation, the Yang-Mills heat equation. The underlying manifold will be smooth, three-dimensional, with a nonempty boundary. We will prove the existence and uniqueness of solutions to this equation, and consider questions about its convergence at infinite time.<br />
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<br />
=== Thursday, March 29, 2007, 12:30-1:50 pm ===<br />
<br />
''Speaker:'' Dr. Bogdan Suceava, Cal State Fullerton<br />
<br />
''Title:'' Curvature invariants in submanifold geometry. New developments.<br />
<br />
''Abstract:'' Recently, in 2005, B.-Y. Chen has proved the most general form of a fundamental inequality with curvature invariants. The first version of his geometric inequality has been given in 1993, and it inspired in the last decade many geometers. The geometric motivation of this study was a classical fundamental problem in Riemannian geometry stated originally by S.-S. Chern, in a monograph from 1968: When does a given Riemannian manifold admit (or does not admit) a minimal immersion into a Euclidean space of arbitrary dimension? This study extends the study of the embedding problem, in the spirit of J. F. Nash's embedding theorem, in terms of curvature invariants. In our talk, we will survey a few recent results in this area and we will present future directions of study in this class of geometric inequalities with new curvature invariants.<br />
<br />
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<br />
=== Thursday, March 8, 2007, 12:30-1:50 pm ===<br />
<br />
''Speaker:'' Dr. Adrian Vajiac<br />
<br />
''Title:'' Overview of Hamilton-Perelman's proof of Poincare Conjecture"<br />
<br />
''Abstract:'' I will present some of the main ideas behind the works of Hamilton and Perelman on Ricci flows, and how these prove Poincare Conjecture. The speaker is far from being an expert in this field, so the exposition will be informal.<br />
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<br />
=== Thursday, March 1, 2007, 12:30-1:50 pm ===<br />
<br />
''Speaker:'' Professor Atanas Radenski<br />
<br />
''Title:'' Digital Support for Abductive Learning in Introductory Computing Courses<br />
<br />
''Abstract:'' Students who grew up browsing the Web are skilled in what is usually referred to as abduction, a reasoning process that starts with a set of specific observations and then generates the best possible explanation of those observations. In order to exploit the abduction skills of contemporary students, I have developed digital CS1/2 study packs that promote and support active learning through abduction, i.e., abductive learning. The study packs integrate a variety of digital resources: online self-guided labs, e-texts, tutorial links, sample programs, quizzes, and slides. These online packs stimulate students to learn abductively by browsing, searching, and performing self-guided lab experiments. In two years of study pack use, the failure rate in the CS1/2 courses at Chapman University has been reduced from 14% to 5%. In surveys conducted at Chapman University in 2005/06, students gave the same high rating of 4.5 (on a 1 to 5 scale) to the CS1 and the CS2 digital study packs. The study packs have been published online at studypack.com and adopted in various institutions.<br />
<br />
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<br />
=== Thursday, February 15, 2007, 12:30-1:50 pm ===<br />
<br />
''Speaker:'' Dr. Mihaela Vajiac<br />
<br />
''Title:'' Harmonic Maps, Loop Groups, and Virasoro Actions, Part II<br />
<br />
''Abstract:'' Continuation of Part I last December: Harmonic maps have been the intense subject in differential geometry for some time now. We will talk about the theory of harmonic maps in Lie groups and the loop groups associated to these spaces of maps. We will then move to describing how this can be thought of as a Riemann-Hilbert Factorization Problem and conclude with the newly found Virasoro action on this space.<br />
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<br />
=== Tuesday, February 6, 2007, 12:30-1:50 pm ===<br />
<br />
''Speaker:'' Dr. Alberto Damiano, Eduard Cech Center, Charles University, Prague.<br />
<br />
''Title:'' Constructing a Dolbeault complex for the Dirac operator in several vector variables.<br />
<br />
''Abstract:'' In this talk I will present the problem of finding a resolution for the system of partial differential equations associated to the classical Dirac operator in several vector variables. It is now widely accepted that such a system constitutes a proper generalization of the Cauchy-Riemann system which defines holomorphic functions of several complex variables, The analysis of the multivariable Dirac operator corresponds then to studying properties of hyperholomorphic functions. So far, mathematicians have attacked the problem of finding compatibiltiy conditions and global properties for the solutions of the system in essentially three different (but strongly related) ways. The first method (see the work of D.C.Struppa, I. Sabadini, F. Colombo et al.) uses techniques of algebraic analysis and Groebner bases to construct a free resolution of the polynomial module given by the cokernel of the symbol of the operator. The second follows the ideas of Baston for case of quaternionic analysis and aims at constructing the so called BGG graph associated to the system. It is an oriented graph in which nodes are representation spaces of a semisimple Lie Algebra [in this case the sum of sl(k) with so(n), where k is the number of variables and n is the dimension of the space] and the arrows are differential operators, the first one being the Dirac operator. The third method is based on some algebraic relations satisfied by the Dirac operator(s) called radial relations.<br />
<br />
Calculations with radial relations lead to the construction of an associative, non commutative algebra called algebra of Megaforms. I will discuss mainly the first two methods and their respective advantages and limitations. In particular, I will show that even when using the representation-theoretic point of view, the aid of a computer algebra system becomes crucial to perform experiments, and in some cases even to prove partial results.<br />
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<br />
=== Thursday, January 18, 2007, 12:30-1:50 pm ===<br />
<br />
''Speaker:'' Professor Graziano Gentili, University of Firenze<br />
<br />
''Title:'' Zeroes and singularities of regular maps of a quaternionic variable.<br />
<br />
''Abstract:'' A geometrical interpretation of a definition originally given by Cullen allows the construction of a new theory of regular functions over the skew field of quaternions. Unlike what happens with other notions of regularity, including the Fueter-regularity, the zero-set and the singular-set of a Cullen-regular function have very nice properties. In this talk we will present the main features of the theory of Cullen-regular functions and show that the zero-sets and singular-sets of such functions consist of isolated points or isolated 2-spheres in the 4-dimensional space of quaternions. <br />
<br />
----</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=MathCS_Seminar_2002&diff=21MathCS Seminar 20022021-02-22T18:42:54Z<p>Jipsen: Created page with "''Seminar Organizer:'' Mihaela Vajiac, ''Webpage maintained by:'' Peter Jipsen == Fall 2002 == '''All seminar talks take place Wednesday mornings in Beckman Hall 402 (corner..."</p>
<hr />
<div>''Seminar Organizer:'' Mihaela Vajiac, ''Webpage maintained by:'' Peter Jipsen<br />
<br />
== Fall 2002 ==<br />
'''All seminar talks take place Wednesday mornings in Beckman Hall 402 (corner of One University Drive and N. Glassell, Orange, CA) at 11 am.'''<br />
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<br />
=== December 11, 2002 ===<br />
<br />
''Speaker:'' Dr. Adrian Vajiac (Chapman University)<br />
<br />
''Title:'' Topological Quantum Field Theory and Invariants of 4-manifolds (Part 2)<br />
<br />
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<br />
=== December 4, 2002 ===<br />
<br />
''Speaker:'' Dr. Adrian Vajiac (Chapman University)<br />
<br />
''Title:'' Topological Quantum Field Theory and Invariants of 4-manifolds (Part 1)<br />
<br />
''Abstract:'' We investigate the relationship between Donaldson and Seiberg-Witten invariants of smooth 4-manifolds,using equivariant localization techniques applied to the corresponding TQFTs that generate these invariants.<br />
This approach is intended to lower the gap between the mathematics and the physics of this subject, possibly leading to a rigorous interpretation of the physics of the generating TQFTs.<br />
<br />
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<br />
=== November 13, 2002 ===<br />
<br />
''Speaker:'' Dr. Mohamed Allali (Chapman University)<br />
<br />
''Title:'' A Covering of the Sphere by a Special Set of Rotations<br />
<br />
''Abstract:'' We will present a method of covering the unit sphere by means of spherical caps of fixed radius. The method based on a set of rotations provides an explicit formula for the number of spherical caps that cover the whole unit sphere and the exact positioning of their centers. To find the optimal number (the minimal number of spherical caps) is still an open problem.<br />
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<br />
=== November 6, 2002 ===<br />
<br />
''Speaker:'' Dr. Mihaela Vajiac (Chapman University)<br />
<br />
''Title:'' "Harmonic Maps and Integrable Systems"<br />
<br />
''Abstract:'' The theory of harmonic maps on Lie groups has <br />
aquired a modern interpretation through integrable systems. We will outline the structual background on harmonic maps into a (compact) Lie group and talk about the arising loop group action and the implications in the theory of integrable systems. <br />
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<br />
=== October 30, 2002 ===<br />
<br />
''Speaker:'' Dr. Andrew Moshier (Chapman University)<br />
<br />
''Title:'' Stably Compact and Related Spaces<br />
<br />
''Abstract:'' Compact Hausdorff spaces, which are well-known to classical mathematicians, have a useful generalization to the setting of non-T1 spaces. The resulting spaces, known as Stably Compact, enjoy many of the useful properties of compact Hausdorff spaces and in fact help to tease apart some concepts that accidentally coindice in the Hausdorff setting. In this talk, we will discuss various topological ideas that lead to characterizations of stable compactness. We will introduce the key result in this area: the Hofmann-Mislove Theorem. Time permitting, we may also discuss interesting topological constructions under which stable compactness is preserved, particularly the construction of the space of Borel measures on an underlying space.<br />
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<br />
=== October 23, 2002 ===<br />
<br />
''Speaker:'' Dr. Peter Jipsen (Chapman University)<br />
<br />
''Title:'' An introduction to residuated KATs and RATs and related algebraic models of computation<br />
<br />
''Abstract:'' In this seminar I will examine some algebraic theories that have been developed in the past half century to reason about algorithms and automata. In particular I will look at Kleene algebras with test and relation algebras with transitive closure. Adding residuation to Kleene algebras gives the algebraic form of Pratt's action logic. It has many of the useful features of relation algebras and is still decidable. I will give a number of finite examples and indicate how to calculate the models on an n-element set.<br />
<br />
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<br />
=== October 9, 2002 ===<br />
<br />
''Speaker:'' Dr. Adrian Vajiac (Chapman University)<br />
<br />
''Title:'' The Geometry and Physics of Fermat's Last Theorem</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=MathCS_Seminar_2003&diff=20MathCS Seminar 20032021-02-22T18:42:14Z<p>Jipsen: Created page with "''Seminar Organizer:'' Mihaela Vajiac, ''Webpage maintained by:'' Peter Jipsen == Fall 2003 == === Wednesday, November 26, 2003, 10 am === ''Speaker:'' Viorel Costeanu (MIT..."</p>
<hr />
<div>''Seminar Organizer:'' Mihaela Vajiac, ''Webpage maintained by:'' Peter Jipsen<br />
<br />
== Fall 2003 ==<br />
<br />
=== Wednesday, November 26, 2003, 10 am ===<br />
<br />
''Speaker:'' Viorel Costeanu (MIT)<br />
<br />
''Title: '' The 2-typical de Rham-Witt complex of the integers<br />
<br />
''Abstract:'' For any ring $A$ and any prime number $p$ there is a construction called the<br />
2-typical de Rham-Witt complex of $A$. It is related to Milnor's $K$-theory,<br />
Quillen's $K$-theory, and topological cyclic homology. This algebraic<br />
structure was studied and quite well understood for $p$ odd. When $p=2$ there<br />
are a few problems that need to be addressed. I will speak about these and<br />
then describe the 2-typical de Rham-Witt complex of the integers.<br />
<br />
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<br />
=== Thursday, November 13, 2003, 2:30 pm ===<br />
<br />
''Speaker:'' Dr. Mihaela Vajiac (Chapman University)<br />
<br />
''Title:'' Quantum Cohomology on Symplectic Manifolds. Properties of the <br />
quantum products.<br />
<br />
''Abstract:'' The quantum products on a symplectic manifold are deformations of the <br />
cup product. The motivation for the theory of Quantum Cohomology comes from <br />
physics, and the mathematical theory has been built rigurously on the theory<br />
of J-holomorphic curves on symplectic manifolds. <br />
We will explore the properties of the quantum products, together with gauge <br />
theoretic techniques developed to anlayze them. <br />
<br />
=== Thursday, November 6, 2003, 2:30 pm ===<br />
<br />
''Speaker:'' Annika Wille (Vanderbilt University; TU Darmstadt, Germany)<br />
<br />
''Title:'' A Gentzen System for Involutive Residuated Lattices<br />
<br />
''Abstract:'' Involutive residuated lattices $\langle L,\wedge,\vee,\cdot,e,'\rangle$ are involutive<br />
lattices with a residuated monoid operation, such that<br />
<br />
$a\cdot b \le c\quad$ iff $\quad a \le (b\cdot c')'\quad$ iff $\quad b \le (c'\cdot a)'$,<br />
<br />
for all $a,b,c \in L$. We can also see an involutive residuated lattice as<br />
a Girard quantale, where the underlying lattice need not be complete.<br />
<br />
A cut-free Gentzen system for Girard quantales is already given by J. Y.<br />
Girard. We will describe a cut-free Gentzen system for involutive<br />
residuated lattices from an algebraic point of view. Finally we conclude<br />
decidability.<br />
<br />
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<br />
=== Thursday, October 30, 2003, 4 pm ===<br />
<br />
''Speaker:'' Dr. Jeff Lawson (Trinity University, Texas; Caltech)<br />
<br />
''Title:'' Lagrangian reduction by symmetry: Variations on a theme<br />
<br />
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<br />
=== Thursday, October 23 ===<br />
<br />
Seminar cancelled<br />
<br />
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<br />
=== Thursday, October 9, 2003, 4 pm ===<br />
<br />
''Speaker:'' Dr. Adrian Vajiac (Chapman University)<br />
<br />
''Title:'' Mathematical Background for Topological Quantum Field Theories"<br />
<br />
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<br />
=== Thursday, October 2, 2003, 4 pm ===<br />
<br />
''Speaker:'' Dr. Andrew Moshier (Chapman University)<br />
<br />
''Title:'' Measure Theoretic, Domain Theoretic and Logical Views of Labelled Markov Processes<br />
<br />
''Abstract:''<br />
Recently, researchers have become increasingly interested in models of<br />
computation in the presence of chance. These models are motivated by<br />
concerns about verification of properties, such as operation within safe<br />
envelopes, when the behavior of the system is influenced by random<br />
events. In one such model, "labelled Markov processes," a system is<br />
modelled as a state machine in which transitions are triggered by<br />
external events, indexed by a set of "labels," resulting in stochastic<br />
internal behavior.<br />
<br />
We will discuss three related ways to think about labelled Markov<br />
processes. In the first, a classical measure theoretic definition<br />
slightly generalizes (discrete time) Markov processes. This yields<br />
concepts of bisimulation and simulation of the states of a process. In<br />
the second, a domain theoretic definition involves the solution of a<br />
certain domain equation. The result can be interpreted as a universal<br />
labelled Markov process. In the third, we relate the domain theoretic<br />
and classical definitions to a logical one by defining a propositional<br />
sequent calculus with semantics definable on any labelled Markov<br />
process. The result characterizes simulation of two states of a labelled<br />
Markov process by inclusion of propositional theories, and bisimulation<br />
by equality of propositional theories. In addition, the very definition<br />
of the sequent calculus derives from the domain equation used to<br />
construct a universal labelled Markov process.<br />
<br />
We will give examples of results that are easily proved using the logic.<br />
Time permitting, we will also apply the domain theoretic and logical<br />
approaches to models of other kinds of probabilistic processes. <br />
<br />
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<br />
=== Thursday, September 25, 2003, 4 pm ===<br />
<br />
''Speaker:'' Dr. Peter Jipsen (Chapman University)<br />
<br />
''Title:'' An introduction to generalized basic logic algebras<br />
<br />
''Abstract:'' Some applications in computing and control theory require a <br />
logic with truthvalues other than the absolute "true" and "false". Many <br />
systems of multi-valued logic have been studied in the past, and quite a <br />
few of them are based on using the interval [0,1] as a set of truth <br />
values. This still leaves much choice as to how truthvalues should be <br />
combined when two statements both hold, but with different degrees of <br />
certainty. The system of Basic Logic was introduced by Petr Hajek in a <br />
series of papers and a book (Metamathematics of Fuzzy Logic, Kluwer, <br />
1998) to give a general framework for a logic that is common to all <br />
multi-valued logics.<br />
<br />
I will review the algebraic version of this logic, called BL-algebra, <br />
relate it to residuated lattices, and show that some of the strong <br />
properties of this logic are also true in various generalized contexts. <br />
In particular I will prove that the extension of BL-algebras with the <br />
so-called projection, gives a class of discriminator algebras, which <br />
explains why the projections have such far reaching consequences for <br />
basic logic. A modification of this result also holds for residuated <br />
lattices with a least element.<br />
<br />
----<br />
<br />
== Summer 2003 ==<br />
'''Seminar talks during the summer take place at various times but still in Beckman Hall 402 (corner of One University Drive and N. Glassell, Orange, CA).'''<br />
<br />
----<br />
<br />
=== Tuesday, June 10, 2003, 2 pm, '''Colloquium Talk''' ===<br />
<br />
''Speaker:'' Prof. Dexter Kozen, Cornell University<br />
(joint work with Mark Hopkins, AMS Inc.)<br />
<br />
''Title:'' Parikh's Theorem in Commutative Kleene Algebra<br />
<br />
''Abstract:'' Parikh's theorem says that every context-free language<br />
is "letter-equivalent" to a regular set. Formally, two sets<br />
are letter-equivalent if any word in one has an anagram<br />
in the other. For example, the CFL $\{a^n b^n \mid n \ge 0\}$<br />
is letter-equivalent to the regular set $(ab)^*$.<br />
<br />
The usual proofs of Parikh's theorem involve an induction<br />
on parse trees of context-free grammars. However, this<br />
result is a special case of a more general result in<br />
commutative Kleene algebra, namely: every commutative<br />
Kleene algebra is uniformly algebraically closed.<br />
Formally, every system of inequalities<br />
<br />
$f_i(x_1,...,x_n) \le x_i,\quad 1 \le i \le n$,<br />
<br />
where the $f_i$ are polynomials in $K[x_1,...,x_n]$ over a commutative<br />
Kleene algebra $K$, has a unique least solution in $K^n$. Moreover,<br />
the components of the solution are given by regular expressions<br />
in the coefficients of the $f_i$.<br />
<br />
The proof involves the definition of a differential operator<br />
$d/dx : K[x] \to K[x]$ on polynomials over a commutative Kleene<br />
algebra and a version of Taylor's theorem<br />
<br />
$f(x+d) = f(x) + d f'(x+d)$.<br />
<br />
----<br />
<br />
=== Wednesday, May 21, 2003, 4 pm ===<br />
<br />
''Speaker:'' Dr. Marcus Kracht (UCLA)<br />
<br />
''Title:'' Weakly Transitive and Semisimple Varieties of Modal Algebras<br />
<br />
''Abstract:'' In polymodal logics one often has to generalize notions from monomodal <br />
logic, eg transitivity and symmetry. It turns out that this can be done <br />
using notions that have originally been invented for monomodal logics. <br />
The notion of weak transitivity (going back to Wim Blok) generalizes the <br />
notion of transitivity in the right way. It shall be shown that many <br />
results in modal logic do not depend on transitivity, they only depend <br />
on weak transitivity. One result is the existence of a deduction theorem <br />
for the global frame consequence, finite equivalentiality, the existence <br />
of many splitting algebras. A variety is cyclic if every operator possesses <br />
(or is included in) a converse. Cyclicity generalizes the notion of <br />
symmetry. It turns out that a variety of modal algebras is semisimple <br />
iff it is both weakly transitive and cyclic iff it is discriminator.<br />
<br />
----<br />
<br />
== Spring 2003 ==<br />
'''All seminar talks take place Thursday afternoons in Beckman Hall 402 (corner of One University Drive and N. Glassell, Orange, CA) at 4 pm.'''<br />
<br />
----<br />
<br />
=== May 8, 2003 ===<br />
<br />
''Speaker:'' Prof. John Yules (Chapman University)<br />
<br />
''Title:'' Design of an Ocean Wave Recorder -- My Sabbatical Project<br />
<br />
''Abstract:'' I plan first to discuss "an oceanographer's view of waves," which encompasses not only wind-generated waves, but also tsunamis and tides. We'll review a wide variety of techniques for making measurements of waves, and I'll show how my plan of attack fits in. Finally, we'll talk about the phenomena that might present themselves for study and perhaps brainstorm about data analysis.<br />
<br />
----<br />
<br />
=== May 1, 2003 ===<br />
Discussion about departmental goals and assessment<br />
<br />
----<br />
<br />
=== April 24, 2003 ===<br />
<br />
''Speaker:'' Dr. Bogdan Suceava (CSU Fullerton)<br />
<br />
''Title:'' Fundamental Inequalities and Strongly Minimal Submanifolds<br />
<br />
''Abstract:'' The classical obstruction to minimal isometric immersions into Euclidean space is $Ric \geq 0.$ A question originated in the work of S.-S.Chern (1968) asked if there are any other curvature Riemannian obstructions to minimal isometric immersion in a space form. The answer has been given by B.-Y. Chen (first form in 1993, general form in 2000). An interesting problem is to see examples of Riemannian manifolds with $Ric<0$ which don't admit any minimal isometric immersion into Euclidean space for any codimension. The proof uses a consequence of Chen's fundamental inequality. The fundamental inequalities have been extended recently in complex space forms, where one of the equality cases bring to our attention a new class of geometric objects: strongly minimal submanifolds. These submanifolds (whose classification is not yet completed) would be the Kaehler submanifolds that best fit in an ambient complex space form.<br />
<br />
----<br />
<br />
=== April 10, 2003 ===<br />
<br />
''Speaker:'' Dr. Mohamed Allali (Chapman University)<br />
<br />
''Title:'' Fourier Transforms and Wavelets (Part 2)<br />
<br />
----<br />
<br />
=== April 3, 2003 ===<br />
<br />
''Speaker:'' Dr. Mohamed Allali (Chapman University)<br />
<br />
''Title:'' Fourier Transforms and Wavelets (Part 1)<br />
<br />
''Abstract:'' Wavelets are now a driving force that has regrouped a<br />
community of mathematicians and engineers sharing representation<br />
techniques. The two-part talk will introduce Fourier Transforms and<br />
Wavelet theory, in particular Multiresolution Analysis.<br />
<br />
----<br />
<br />
=== March 27, 2003 ===<br />
<br />
''Speaker:'' Dr. Mihaela Vajiac (Chapman University)<br />
<br />
''Title:'' Lie Groups, Loop Groups in Lie Groups and Harmonic Maps (Part 3)<br />
<br />
----<br />
<br />
=== March 20, 2003 ===<br />
<br />
''Speaker:'' Dr. Mihaela Vajiac (Chapman University)<br />
<br />
''Title:'' Lie Groups, Loop Groups in Lie Groups and Harmonic Maps (Part 2)<br />
<br />
----<br />
<br />
=== March 13, 2003 ===<br />
<br />
''Speaker:'' Dr. Mihaela Vajiac (Chapman University)<br />
<br />
''Title:'' Lie Groups, Loop Groups in Lie Groups and Harmonic Maps (Part 1)<br />
<br />
----<br />
<br />
=== March 6, 2003 ===<br />
<br />
=== February 27, 2003 ===<br />
<br />
''Speaker:'' Dr. Peter Jipsen (Chapman University)<br />
<br />
''Title:'' An online database of ordered algebraic structures (Part 2)<br />
<br />
----<br />
<br />
=== February 20, 2003 ===<br />
<br />
''Speaker:'' Dr. Peter Jipsen (Chapman University)<br />
<br />
''Title:'' An online database of ordered algebraic structures (Part 1)<br />
<br />
''Abstract:'' Research in ordered algebraic structures has grown from the classical<br />
areas of ordered groups, rings, and fields to the study of a wide<br />
variety of classes of partially ordered algebras, where the order takes<br />
the form of (join- or meet-) semilattices, lattices, or Boolean<br />
algebras. In addition, subclasses determined by various completeness<br />
properties and residuation properties have received considerable<br />
attention, motivated by studies in algebraic logic, topology, and<br />
theoretical computer science. While researchers are familiar with the<br />
structures in their areas of expertise, it is no small task to be<br />
informed about the terminology, definitions, basic properties and<br />
relationships between the many classes of structures in this growing field.<br />
<br />
This talk will present a preliminary version of an online database that<br />
aims to (eventually) survey most classes of ordered algebraic structures<br />
that have appeared in the literature. At minimum, a record for a class<br />
contains its name, (several) definition(s), some of the basic properties<br />
and results about the class, and the position of the class in this<br />
hierarchy relative to its ``nearest'' sub- and superclasses. Most of the<br />
classes are categories in a natural way, and concepts from category<br />
theory are used to express structure preserving relationships between<br />
different classes. Currently the database contains around a hundred<br />
classes from action algebras to weakly representable relation algebras.<br />
Although intended mainly as a reference for researchers, with citations<br />
to the literature for further detail, the database aims to store<br />
definitions in machine-readable form to allow additional processing with<br />
computational tools. It will also provide access to families of examples<br />
and (where feasible) implementations of algorithms for computable<br />
syntactic or semantic properties of a given class. For example, if a<br />
class has a decidable equational theory, an implementation of a decision<br />
procedure may be included in the entry for the class. Tools for<br />
visualizing (parts of) the partial order structure of specific examples<br />
and of the hierarchy of classes will be discussed, as well as recent<br />
significant online developments such as MathML and XML transformation<br />
tools that play a role in our approach.<br />
<br />
Much work remains to be done to give this database the breadth and<br />
consistency that would ensure it is a useful research tool and is<br />
helpful to students entering this area. In fact, in a successful<br />
scenario, this project will not be completed at some stage, but will<br />
continue to grow in a collaborative style, thereby ensuring that the<br />
information in the database remains up-to-date.<br />
<br />
----<br />
<br />
=== February 13, 2003 ===<br />
<br />
''Speaker:'' Dr. Andrew Moshier (Chapman University)<br />
<br />
''Title:'' Stably Compact Spaces Predicatively Understood (Part 2)<br />
<br />
----<br />
<br />
=== February 6, 2003 ===<br />
<br />
''Speaker:'' Dr. Drew Moshier (Chapman University)<br />
<br />
''Title:'' Stably Compact Spaces Predicatively Understood (Part 1)<br />
<br />
''Abstract:'' Stably compact spaces are suitable for investigating relationships between classical mathematics and computation because they include compact regular spaces and topological spaces that arise in domain theory. Proofs of many theorems involving stably compact spaces, however, depend on the axiom of choice and other non-constructive principles. This presents a problem if we are to understand these spaces computationally. The axiom of choice comes into play when we need to speak about existence of points in a space. Impredicativity (roughly, non-constructive quantification over powersets) comes into play when we need to speak about compactness, and more generally about arbitrary collections of opens.<br />
<br />
We briefly motivate the concern about predicativity and constructivity, and then consider two alternatives to stably compact spaces: stably compact locales and stable sequent calculi. The former can be thought of as stably compact spaces "without points." The latter can be thought of representations of compactness information in stably compact locales. We sketch proofs showing that stably compact spaces, stably compact locales and stable sequent calculi form equivalent categories, isolating the use of non-constructive principles in these equivalences. To illustrate the point, we also give an entirely predicative proof of Tychonoff's theorem for stable calculi (a product of stable calculi is a stable calculus).</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=MathCS_Seminar_2004&diff=19MathCS Seminar 20042021-02-22T18:41:45Z<p>Jipsen: Created page with "''Seminar Organizer:'' Mihaela Vajiac, ''Webpage maintained by:'' Peter Jipsen == Fall 2004 == === Thursday, December 2, 2004, 3 pm === ''Speaker:'' Dr. Mohamed Allali ''T..."</p>
<hr />
<div>''Seminar Organizer:'' Mihaela Vajiac, ''Webpage maintained by:'' Peter Jipsen<br />
<br />
== Fall 2004 ==<br />
<br />
=== Thursday, December 2, 2004, 3 pm ===<br />
<br />
''Speaker:'' Dr. Mohamed Allali<br />
<br />
''Title:'' Interpolation and Equidistribution on the unit sphere<br />
<br />
''Abstract:'' The problem of generating a large number of points on the<br />
sphere has many applications in various fields of computation such as<br />
quadrature, placing grids on S2, tomography, coding theory, etc. This<br />
talk will introduce different methods of equidistributing points on the<br />
sphere. Moreover, of practical importance is the problem of<br />
interpolating scattered data on the sphere. Strictly positive definite<br />
functions shall be introduced and connected to the interpolation<br />
problem.<br />
<br />
----<br />
<br />
=== Thursday, November 18, 2004, 3 pm ===<br />
<br />
''Speaker:'' Prof. Mihaela Vajiac<br />
<br />
''Title:'' Harmonic Maps on SU(n) and Virasoro actions, part II<br />
<br />
Joint work with Professor Karen Uhlenbech, UT Austin<br />
<br />
''Abstract:'' This introductive talk covers the interaction between Harmonic<br />
Maps, Loop Groups and Integrable Systems.<br />
<br />
We continue with the construction of the Virasoro algebra in the SU(n)<br />
case.<br />
<br />
----<br />
<br />
=== Thursday, October 28, 2004, 3 pm ===<br />
<br />
''Speaker:'' Prof. Mihaela Vajiac<br />
<br />
''Title:'' Harmonic Maps on SU(n) and Virasoro actions<br />
<br />
Joint work with Professor Karen Uhlenbech, UT Austin<br />
<br />
''Abstract:'' This introductive talk covers the interaction between Harmonic Maps, Loop Groups and Integrable Systems.<br />
<br />
We will continue next thursday with the construction of the Virasoro algebra in the SU(n) case.<br />
<br />
----<br />
<br />
== Spring 2004 ==<br />
'''All seminar talks take place Thursday afternoons in Beckman Hall 402 (corner of One University Drive and N. Glassell, Orange, CA).'''<br />
<br />
=== Thursday, April 29, 2004, 4 pm ===<br />
<br />
''Speaker:'' Dr. Joanne Walters-Wayland<br />
<br />
''Title:'' $G_{\delta}$-density in a pointfree setting<br />
<br />
''Abstract:'' I shall endeavour to give a short history of, and motivation for<br />
studying, "generalized topoplogy". I shall also attempt to highlight the<br />
beauty of this theory by considering $G_{\delta}$-density in this setting. In<br />
particular, I will introduce the cozero part of a frame - the cozeros are<br />
essential in understanding many concepts especially when dealing with<br />
complete regularity and related notions. <br />
<br />
----<br />
<br />
=== Thursday, April 8, 2004, 1:30 pm ===<br />
<br />
''Speaker:'' Dr. Catalin Zara (Penn State)<br />
<br />
''Title:'' Hamiltonian GKM Spaces: From Geometry To Combinatorics, And Back.<br />
<br />
----<br />
<br />
=== Thursday, April 1, 2004, 2:45 pm ===<br />
<br />
''Speakers:'' Catherine Parsons, Vicki Shultz and Zack Wheatly (Chapman University)<br />
<br />
''Title:'' Morphing, Warping and SVD Through Linear Algebra.<br />
<br />
''Abstract:'' Linear Algebra is used throughout Digital Image Processing (DIP) for both effects and compression. Morphing and warping, two techniques in DIP used to make one image "transform" into another, and Singular Value Decomposition (SVD) are examples of this which we will present in this talk. Morphing fades one image into another, while warping stretches and skews the images based off chosen lines. SVD takes an original image, breaks it into three distinct matrices, and extracts enough pertinent information to still<br />
recreate the image while using less memory. Through our presentation we<br />
will show how these three techniques in DIP can be achieved with the basic tools of Linear Algebra.<br />
<br />
----<br />
<br />
=== Thursday, March 18, 2004, 3 pm ===<br />
<br />
''Speaker:'' Noah Salvaterra (Indiana University, Bloomington)<br />
<br />
''Title:'' A Brief Introduction to Khovanov Homology<br />
<br />
''Abstract:'' By a modification of Kauffman's bracket for a link diagram one can construct a chain complex of graded vector spaces. Just as a renormalization of the Kauffman bracket leads to a link invariant, the Jones polynomial, a similar renormalization of this complex gives rise to interesting homologies which are actually link invariants. While in fact the Jones polynomial arises as the graded Euler characteristic in this construction, the Poincare polynomial of these homologies is a strictly stronger invariant.<br />
<br />
I hope to give a brief overview of this construction with lots of pictures, filling in the necessary knot theory along the way.<br />
<br />
----<br />
<br />
=== Thursday, March 11, 2004, 3 pm ===<br />
<br />
''Speaker:'' Dr. Mihaela Vajiac (Chapman University)<br />
<br />
''Title:'' Quantum Cohomology and Quantum Products.<br />
<br />
''Abstract:'' The theory of quantum cohomology and Gromov-Witten invariants was<br />
first developed by Witten and has been the subject of<br />
active research in algebraic and symplectic geometry.<br />
In my talk, gauge theory techniques and the theory of flat<br />
connections are used to prove that the small quantum product is a<br />
gauge theoretic deformation of the cup product on a symplectic<br />
manifold M and to construct a moduli space of products on a<br />
vector space which are associative, commutative, Frobenius, and have<br />
unit (we will call these quantum-type products). <br />
<br />
----<br />
<br />
=== Thursday, February 25, 2004, 3 pm ===<br />
<br />
Meeting on assessment of GE Calculus<br />
<br />
----<br />
<br />
=== Thursday, February 19, 2004, 3 pm ===<br />
<br />
Meeting to discuss GE, precalculus textbook adoption.<br />
<br />
----<br />
<br />
=== Thursday, February 12, 2004, 3 pm ===<br />
<br />
''Speaker:'' Dr. Peter Jipsen (Chapman University)<br />
<br />
''Title:'' Representable l-groups are algebras of binary relations, and representable finite GBL-algebras are commutative.<br />
<br />
''Abstract:'' It is shown that any representable l-group G is isomorphic to a set of binary relations $R(G)$ closed under union, intersection, composition and residuals. The identity element of the l-group corresponds to the partial order relation rather than the diagonal relation, and the collection of binary relations is not closed under relation converse. However this construction never-the-less shows that the variety of representable l-groups is contained in the class of all binary relations closed under union, intersection, composition and residuals. It is interesting to note that, in contrast to the variety of representable l-groups, the latter class is not finitely axiomatizable. The construction shows that representable l-groups are subreducts of relation algebras with an additional constant, and leads to a number of interesting problems regarding the algebras of binary relations generated by $R(G)$ if we also include relation converse and/or complementation as basic operations.<br />
<br />
In the second part of the talk we will show that representable generalized basic logic algebras are commutative, hence simply BL-hoops. Some possible generalizations of this result will also be discussed.</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=MathCS_Seminar_2005&diff=18MathCS Seminar 20052021-02-22T18:41:13Z<p>Jipsen: Created page with "''Seminar Organizer:'' Mihaela Vajiac, ''Webpage maintained by:'' Peter Jipsen == Fall 2005 == '''All seminar talks take place in Argyros Forum 211.''' ---- === Thursday, D..."</p>
<hr />
<div>''Seminar Organizer:'' Mihaela Vajiac, ''Webpage maintained by:'' Peter Jipsen<br />
<br />
== Fall 2005 ==<br />
'''All seminar talks take place in Argyros Forum 211.'''<br />
<br />
----<br />
<br />
=== Thursday, December 7, 2005, 12-1 pm ===<br />
<br />
''Speaker:'' Professor Achim Jung, University of Birmingham<br />
<br />
''Title:'' Extending valuations to measures<br />
<br />
''Abstract:'' Many theorems in measure theory are about extending a "proto-measure" to<br />
a full measure, where "proto" means that the given function assigns a<br />
volume only to some measureable sets. Computer scientists became<br />
interested in one particular instance of this where the proto-measure is<br />
defined on the open sets of a topological space. Such proto-measures had<br />
been looked at before under the name "valuations".<br />
<br />
In my talk I will try to explain why valuations are particularly<br />
interesting from a computer science point of view, and I will prove an<br />
extension theorem using classical theorems from analysis. This proof<br />
works only for compact ordered spaces, and so I will get an excuse for<br />
explaining why these are of interest to computer scientists, too.<br />
<br />
The talk is based on joint work with Klaus Keimel.<br />
<br />
----<br />
<br />
=== Thursday, November 30, 2005, 12-1 pm ===<br />
<br />
''Speaker:'' Dr. Mihaela Vajiac<br />
<br />
''Title:'' Harmonic Maps and Loop Groups on SU(2).<br />
<br />
----<br />
<br />
=== Thursday, November 29, 2005, 12-1 pm ===<br />
<br />
''Speaker:'' Arek Goetz, University of San Francisco<br />
<br />
''Title:'' Multimedia online learning environment as a tool in teaching<br />
calculus and in research in geometric dynamical systems<br />
<br />
----<br />
<br />
=== Thursday, November 9, 2005, 12-1 pm ===<br />
<br />
''Speaker:'' Dr. Mihaela Vajiac<br />
<br />
''Title:'' Quantum Cohomology in Symplectic Geometry <br />
<br />
----<br />
<br />
=== Thursday, October 26, 2005, 12-1 pm ===<br />
<br />
''Speaker:'' Dr. Adrian Vajiac<br />
<br />
''Title:'' Equivariant Cohomology<br />
<br />
----<br />
<br />
=== Thursday, October 12, 2005, 12-1 pm ===<br />
<br />
''Speaker:'' Dr. Adrian Vajiac<br />
<br />
''Title:'' The Global Aspect of the Parallelism Axiom<br />
<br />
----<br />
<br />
=== Thursday, October 5, 2005, 12-1 pm ===<br />
<br />
''Speaker:'' Dr. Peter Jipsen<br />
<br />
''Title:'' Complex algebras of groups and Boolean algebras<br />
<br />
''Abstract:'' Given a group $G$, the complex algebra Cm$(G)$ is defined by<br />
$(P(G),\cup,\sim,\emptyset,*,^{-1},\{e\})$, where <br />
<br />
$X*Y=\{xy : x \in X, y \in Y\}$ and $X^{-1}=\{x^{-1} : x \in X\}$<br />
<br />
for any subsets $X,Y$ of $G$. Likewise, for a<br />
Boolean algebra $B$, the complex algebra Cm$(B)$ is defined by<br />
$(P(B),\cup,\sim,\emptyset,+,-,\{0\})$, where $+,-$ are the lifted<br />
versions of the Boolean join and complementation of $B$. It is<br />
well-known that the class of all complex algebras of groups is<br />
nonfinitely axiomatizable and undecidable. The corresponding problems<br />
for the variety HBA generated by complex algebras of Boolean algebras<br />
have not yet been resolved. As a contribution in this direction, we<br />
find a number of identities that hold in all complex algebras of<br />
Boolean algebras, and we prove that if a Boolean algebra with<br />
additional operations $+,-,0$ has $\le 24$ elements then it will be in the<br />
variety HBA iff it satisfies these identities.<br />
<br />
----<br />
<br />
=== Thursday, September 29, 2005, 3 pm ===<br />
<br />
''Speaker:'' Prof. Atanas Radenski<br />
<br />
''Title:'' Can Introductory Computer Science Be Relieved From the Complexity<br />
of Commercial Languages? A "Python First, Java Second" Approach to<br />
CS1/CS2<br />
<br />
''Abstract:''<br />
In this talk, I will advocate the need for, and the benefits from, a<br />
dual-language approach to the introductory computer science course<br />
sequence, commonly referred to as CS1/CS2. I will describe my<br />
implementation of a "Python First, Java Second" approach that has been<br />
used at Chapman University since the fall of 2004: A gentle CS1 course<br />
builds core knowledge using the Python language, while a subsequent<br />
comprehensive CS2 course upgrades and extends this knowledge using a<br />
mainstream language, Java.<br />
<br />
To support "Python first, Java second" courses, I have created<br />
comprehensive online study packs that provide complete coverage for all<br />
course activities. Both study packs feature detailed self-guided lab<br />
assignments and honor lab report system. The study packs reduce the need<br />
for face-to-face activities thus facilitating students with busy class<br />
and work schedules. Both study packs are installed on a Moodle server.<br />
<br />
----<br />
<br />
== Spring 2005 ==<br />
'''All seminar talks take place in Beckman Hall 402.<br />
<br />
=== Thursday, April 14, 2005, 3 pm ===<br />
<br />
''Speaker:'' Dr Adrian Vajiac<br />
<br />
''Title:'' Topological Invariants of 4-manifolds<br />
<br />
----<br />
<br />
=== Thursday, April 7, 2005, 4 pm ===<br />
<br />
''Speaker:'' Dr Scott Baldridge (Louisiana State University)<br />
<br />
''Title:'' On symplectic 4-manifolds with prescribed fundamental group<br />
<br />
''Abstract:''<br />
In this talk I will discuss minimizers of the function $f=a\chi+b\sigma$ on the class of all<br />
symplectic 4--manifolds with prescribed fundamental group $G$ ($\chi$ is the Euler<br />
characteristic, $\sigma$ is the signature, and $a,b\in \BR$). The values of $a,b$ for which<br />
the function $f$ has a lower bound have some surprising features. I will discuss these<br />
features and describe some examples of manifolds which minimize $\chi$.<br />
<br />
----<br />
<br />
=== Thursday, March 31, 2005, 3 pm ===<br />
<br />
''Speaker:'' Dr Andrew Moshier (Chapman University)<br />
<br />
''Title:'' Synthetic Topology and Semantics of Exceptions. Part II<br />
<br />
----<br />
<br />
=== Thursday, March 17, 2005, 3 pm ===<br />
<br />
''Speaker:'' Dr Andrew Moshier (Chapman University)<br />
<br />
''Title:'' Synthetic Topology and Semantics of Exceptions.<br />
<br />
''Abstract:''<br />
In the late 1980's, Mike Smyth developed a series of analogies between computational and topological ideas that have come to be known as "Smyth's dictionary". Recently the dictionary has been extended along various lines leading to research programs called "Synthetic Topology" (pursued especially by Martin Escardo and Andre Bauer) and "Abstract Stone Duality" (pursued by Paul Taylor). In this talk, we will introduce the basics of Smyth's dictionary, outline some of the newer directions of this research (borrowing heavily from Escardo and Taylor), and mention a further recent development that brings bitopological concepts into the story and sheds some promising light on how computational exceptions fit into Smyth's analogies. <br />
<br />
----<br />
<br />
=== Thursday, February 17, 2005, 3 pm ===<br />
<br />
''Speaker:'' Dr Peter Jipsen (Chapman University)<br />
<br />
''Title:'' On congruences in Residuated Kleene algebras<br />
<br />
''Abstract:'' Kleene algebras have a long history in Computer Science, with applications in formal foundation for automata theory, regular grammars, semantics of programming languages and other areas.<br />
<br />
However the algebraic structure of Kleene algebras has not been studied as extensively. This is partly because the class of all Kleene algebras is a quasivariety but not a variety, i.e. it can be defined by strict Horn formulas but not by identities. If we add the quite natural operations of left and right residuals for the Kleene product, we get the variety of residuated Kleene algebras (also called action algebras by V. Pratt, 1990 and D. Kozen, 1994). Until recently it was not even known if the variety of residuated Kleene algebras is congruence distributive. Since this property has many useful algebraic consequences, it is certainly of interest that (a noncommmutative version of) a result in algebraic logic by C. van Alten and J. Raftery, 2004, based on a description of congruence filters by W. Blok and J. Raftery, implies that the congruence lattice of any residuated Kleene algebra is distributive.<br />
<br />
We give an overview of this result in the present setting and explore some of its consequences for the lattice of varieties of residuated Kleene algebras. In particular we show that this lattice contains uncountably many varieties covering the Boolean variety.<br />
<br />
----<br />
<br />
=== Thursday, February 10, 2005, 3 pm ===<br />
<br />
''Speaker:'' Dr. Mohamed Allali<br />
<br />
''Title:'' Interpolation and Equidistribution on the unit sphere, part II.<br />
<br />
''Abstract:'' The problem of generating a large number of points on the<br />
sphere has many applications in various fields of computation such as<br />
quadrature, placing grids on S2, tomography, coding theory, etc.</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=MathCS_Seminar_2006&diff=17MathCS Seminar 20062021-02-22T18:40:37Z<p>Jipsen: Created page with "== Fall 2006 == '''All seminar talks take place in Beckman Hall 402 (corner of One University Drive and N. Glassell, Orange, CA).''' === Thursday, November 30, 2006, 12:30-1:..."</p>
<hr />
<div>== Fall 2006 ==<br />
'''All seminar talks take place in Beckman Hall 402 (corner of One University Drive and N. Glassell, Orange, CA).'''<br />
<br />
=== Thursday, November 30, 2006, 12:30-1:50 pm ===<br />
<br />
''Speaker:'' Dr. Mihaela Vajiac<br />
<br />
''Title:'' Harmonic Maps and Loop Groups<br />
<br />
''Abstract:'' Harmonic maps have been the intense subject in differential geometry for some time now. We will talk about the theory of harmonic maps in Lie groups and the loop groups associated to these spaces of maps. We will then move to describing how this can be thought of as a Riemann-Hilbert Factorization Problem and conclude with the newly found Virasoro action on this space .<br />
<br />
----<br />
<br />
=== Wednesday, November 15, 2006, 12:30-1:50 pm ===<br />
<br />
''Speaker:'' Halina Goetz<br />
<br />
''Title:'' Challenges and success stories in teaching preparatory courses<br />
<br />
''Abstract:'' The speaker summarizes her experience teaching remedial courses in various settings, she will outline misconceptions about tutoring, will and some challenges in teaching Mathematics for Elementary Teachers by comparing and contrasting the delivery of the course at other institutions. She will conclude the talk with tangible and concrete steps for improving the overall teaching results in remedial and MATH 206 class.<br />
<br />
----<br />
<br />
=== Thursday, November 2, 2006, 12:30-1:50 pm ===<br />
<br />
''Speaker:'' Dr. Peter Jipsen<br />
<br />
''Title:'' Involutive residuated frames with applications to decidability<br />
<br />
(joint work with Dr. Nikolaos Galatos, Japan Advanced Institute for Science and Technology)<br />
<br />
''Abstract:'' We consider frames for involutive residuated lattices. We use them to prove a general cut-elimination result for this variety and derive the finite model property for classical substructural logics (without any assumption of commutativity or cyclicity). Connections with relation algebras are highlighted, and we examine several constructions on frames (various unions and products) that illustrate how involutive frames provide a unifying perspective for involutive lattices.<br />
<br />
----<br />
<br />
=== Thursday, October 26, 2006, 12:30-1:50 pm ===<br />
<br />
''Speaker:'' Dr. Peter Jipsen<br />
<br />
''Title:'' Residuated (Kripke) frames<br />
<br />
(joint work with Dr. Nikolaos Galatos, Japan Advanced Institute for Science and Technology)<br />
<br />
''Abstract:'' The notion of frames from modal logic has been generalized in a number of different ways. We present some background on residuated lattice ordered groupoids,<br />
FL-algebras and several important subvarieties (involutive, cyclic, classical, commutative, distributive, Boolean). The represention of lattices via Galois correspondences and the concept of nucleus are shown to lead naturally to the notion of nuclear Galois relation. This results in the definition of residuated frames as a suitable generalization of Kripke semantics for FL-algebras. <br />
<br />
----<br />
<br />
=== Thursday, October 19, 2006, 12:30-1:50 pm ===<br />
<br />
''Speaker:'' Dr. M. Andrew Moshier<br />
<br />
''Title:'' Hofmann-Mislove Theorems in Bitopological Settings<br />
<br />
''Abstract:'' The Hofmann-Mislove Theorem for sober topological spaces establishes a valuable connection between compact subsets and certain filters of opens, roughly speaking, by extending the bijection between points and completely prime filters that characterizes sober spaces. The theorem has proved to be very useful in domain theory and other areas of topology. <br />
<br />
In the first part of this talk, we will consider ways to interpret the classical result as well as its frame-theoretic analogue. Following that, we will discuss new results on bitopological spaces and their Stone duals.<br />
<br />
''N.B''. This talk is self-contained. Although last seminar talk "On the Bitopological Nature of Stone Duality" provides some motivation, I will not use any technical ideas from that talk.<br />
<br />
----<br />
<br />
=== Thursday, September 28, 2006, 12:30-1:30 pm ===<br />
<br />
''Speaker:'' Dr. M. Andrew Moshier<br />
<br />
''Title:'' On the Bitopological Nature of Stone Duality<br />
<br />
''Abstract:'' <br />
The relationship between classical Stone Duality and the theory of frames is much more subtle than one is often lead to believe. In particular, Stone Duality has to do with bounded distributive lattices (and more specially, Boolean rings) that need not be complete, whereas a frame is a special sort of complete lattice. So Stone's original results, as well as several more recent Stone-type dualities, do not actually generalize, nor specialize, the duality between spaces and frames (here refered to as "Papert/Isbell duality").<br />
<br />
We provide a uniform treatment of Stone-type dualities as well as Papert/Isbell duality, both as specializations of a general concrete adjunction. Toward this end, we introduce the category of "d-frames" as the duals of bi topological spaces. In frames, two distinct notions of order are conflated: a frame is a certain kind of dcpo (information ordered) and is a certain kind of distributive lattice (logically ordered). In d-frames, the symmetry between information and logic breaks naturally. It is this broken symmetry on the "frame-theoretic" side along with the asymmetry of bispaces on the "topological side" that allows for a uniform treatment of Stone and Isbell duality.<br />
<br />
----<br />
<br />
=== Thursday, September 21, 2006, 12:30-1:30 pm ===<br />
<br />
''Speaker:'' Dr. Raymundo Marcial Romero<br />
<br />
''Title:'' A computational framework for exact real number arithmetic.<br />
<br />
''Abstract:'' Almost every mechanical device to do real number calculations uses the well-known floating-point arithmetic. However floating-point arithmetic cannot represent every real number in an exact form. Hence, in a calculation a rounding is done to the closest floating-point number. Although this kind of representation is useful for a large number of calculations, there are other frameworks in which more accurate solutions are required. Exact real number arithmetic is a different paradigm to do real number computation in an "exact" form. In this talk we sketch exact real number arithmetic and present a programming language to work with it.<br />
<br />
----<br />
<br />
=== Thursday, September 14, 2006, 12:30-1:30 pm ===<br />
<br />
''Speaker:'' Professor Daniele Struppa <br />
<br />
''Title:'' Algebraic Analysis of Dirac Systems<br />
<br />
----</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=MathCS_Seminar_2008&diff=16MathCS Seminar 20082021-02-22T18:37:11Z<p>Jipsen: Created page with "== Fall 2008 == The seminar talks are usually in Beckman Hall 207 (corner of [http://maps.google.com/maps?q=N+Glassell+St+%26+University+Dr,+Orange,+CA+92866,+USA&sa=X&oi=map..."</p>
<hr />
<div>== Fall 2008 ==<br />
<br />
The seminar talks are usually in Beckman Hall 207 (corner of [http://maps.google.com/maps?q=N+Glassell+St+%26+University+Dr,+Orange,+CA+92866,+USA&sa=X&oi=map&ct=title N. Glassell St and University Drive], Orange, CA 92866)<br />
----<br />
<br />
=== Friday, December 5th, at 1:00pm in BK207 ===<br />
<br />
''Speaker:'' Dr.Martha Dussan, Universidade de Sao Paulo & UCI<br />
<br />
''Title:''<br />
A characterization of Christoffel transform in the Split-Quaternions<br />
<br />
''Abstract:''<br />
This talk is focusing to characterize the Christoffel pairs of timelike isothermic surfaces in the split-quaternions $H' = \mathbb R^4_2$. When we restrict the ambient space to the imaginary split-quaternions $Im H' = \mathbb R^3_2$, we also characterize that kind of pair through of the existence of an integranting factor. This a joint work with Prof. M. Magid.<br />
<br />
----<br />
<br />
=== Thursday, November 20th, at 1:00pm in BK207 ===<br />
<br />
''Speaker:'' Dr. David Pincus , <br />
Chapman University, <br />
<br />
''Title:''<br />
Fractal Dynamics in Interpersonal Processes<br />
<br />
''Abstract:''<br />
This presentation will review a line of research investigating a theoretical model of interpersonal dynamics based on processes of self-organization and complexity theory. Empirical investigations of the complexity of patterns of repetition in verbal turn-taking behaviors during conversations using various measures of entropy (topological, information, and fractal dimension) have consistently demonstrated that interpersonal dynamics exhibit fractal patterns characteristic of far-from-equilibrium conditions at the “edge-of-chaos.” For example, statistical fits between an inverse-power-law (IPL) model and long-sequence patterning in conversations have ranged from R2 = .87 to R2 = .99. These results have been found in conversations within group therapy, family therapy, and experimentally-created relationships among strangers. Furthermore, a statistical model of interpersonal closeness, conflict, and control accounted for a combined 48% of the variance in pattern repetition (structure) within the IPL above and beyond speaker base-rates (combinatorial probabilities). Finally, a series of experimental investigations has demonstrated that the fractal dimension of turn-taking patterns within small groups shifts significantly in the direction of rigidity depending upon levels of internal conflict within group members. In addition to some practical significance for applied psychology, these results provide for a number of possible theoretical integrations, within psychology between psychology and other scientific domains. Key areas for discussion will include: a) The potential to derive more formal and specific mathematical models (e.g., differential equation models) to simulate relationship development over time and under various conditions; b) Graphics programs that could more effectively display the fractals underlying these conversations; and c) improved statistical procedures that could better identify processes such as bifurcations, transients, and changes in the contributions of individuals to overall group structure during conversations.<br />
<br />
----<br />
<br />
=== Thursday, November 6th, at 4:00pm in BK207 ===<br />
<br />
''Speaker:'' Dr. Adrian Vajiac, <br />
Chapman University, <br />
<br />
''Title:''<br />
Algebraic Analysis of ElectroMagnetism<br />
<br />
''Abstract:''<br />
In recent years, techniques from computational algebra have become important to render effective general results in the theory of Partial Differential Equations. Following our work with D.C. Struppa, I. Sabadini, F. Colombo, and M. Vajiac, we will present how these tools can be used to discover and identify important properties of several physical systems of interest such as Electromagnetism and Abelian Instantons.<br />
<br />
----<br />
<br />
=== Thursday, October 23rd, at 4:00pm in BK207 ===<br />
<br />
''Speaker:'' Professor Roman A. Polyak, <br />
Department of Mathematical sciences & SEOR Department, George Mason University<br />
<br />
''Title:''<br />
Nonlinear Equilibrium vs. Linear Optimization<br />
<br />
''Abstract:''<br />
We consider the Generalized Walras-Wald Equilibrium (GE) as an alternative to Linear Programming (LP) approach for optimal recourse allocation. There are two fundamental differences between the GE and LP approach for the best resource allocation.<br />
First, the prices for goods (products) are not fixed as they are in LP; they are functions of the production output.<br />
Second, the factors (resources) used in the production process are not fixed either; they are functions of the prices for the resources.<br />
It was shown that under natural economic assumptions on both prices and factors vector functions the GE exists and unique. <br />
Finding the GE is equivalent to solving a variational inequality with a strongly monotone operator on nonnegative octants of the primal and dual spaces. For solving the variational inequality a projected pseudo-gradient method was introduced , his global convergence with Q-linear rate was proven an its computational complexity was estimated. <br />
The method can be viewed as a natural pricing mechanism for establishing an economic equilibrium.<br />
<br />
About this week's speaker: Roman A.Polyak, received Ph. D in mathematics from Moscow Central Institute of Mathematics and Economics at the Soviet Academy of Sciences.<br />
After emigration from the former Soviet Union he was a visiting scientist at the Mathematical Sciences Department at the T.J. Watson Research Center IBM. <br />
Since 1995 Dr. Polyak is a Professor of Mathematics and Operations Research at George Mason University.<br />
He is an author and co-author of six monographs and chapters of books and published more than sixty papers in refereed professional journals. <br />
His area of expertise is Linear and Nonlinear programming , game theory and mathematical economics. <br />
He received several NSF and NASA Awards as well as the Fulbright Scholarship Award for his work on Nonlinear Rescaling Theory and Methods in constrained optimization.<br />
<br />
----<br />
<br />
=== Thursday, October 16th, at 4:00pm in BK207 ===<br />
<br />
''Speaker:'' Dr. Mihaela Vajiac, <br />
Chapman University, <br />
<br />
''Title:''<br />
Hartogs Phenomena and Antisyzygies for Systems of Differential Equations<br />
<br />
''Abstract:''<br />
This work, in collaboration with A. Damiano, D. Struppa, and A. Vajiac introduces the notion of antisyzygies, which studies the inverse problem of finding a system of PDEs, given compatibility conditions. The system obtained possesses the property of removability of compact singularities. We also write explicit computations in the cases of the Cauchy-Fueter system and Maxwell’s system for electromagnetism, and we conclude with a study of systems of non-maximal rank.<br />
<br />
----<br />
<br />
=== Thursday, October 2nd, at 4:00pm in BK207 ===<br />
<br />
''Speaker:'' Dr. Cyril Rakovski, <br />
Chapman University, <br />
<br />
''Title:''<br />
Unweighted analysis of counter-matched case-control data. <br />
<br />
''Abstract:''<br />
Informative sampling based on counter-matching risk set subjects on an exposure variable has been shown to be an efficient alternative to simple random sampling when the counter-matching variable is correlated with the variable of interest; however, the opposite is true when the counter-matching variable is independent of the variable of interest. For given counter-matched data, we consider a naive analysis of the effect of a dichotomous covariate on the disease rates that ignores the underlying sampling design and its corresponding effect on the analytic expression of the partial likelihood. We provide analytical expressions for the bias and variance and show that under mild common conditions such an analysis is clearly advantageous over the standard "weighted" approach. The efficiency gains could be large and are inversely related to the prevalence of the counter-matching variable. Finally, we ascertain that departures from the required assumptions entail biased estimates and provide numerical values for the bias for common scenarios.<br />
<br />
----<br />
<br />
=== Thursday, September 25th, at 4:00pm in BK207 ===<br />
<br />
''Speaker:'' Prof. Arek Goetz, <br />
San Francisco State University<br />
<br />
''Title:''<br />
The interplay of symbolic computing with geometry in dynamical systems arising from theoretical electrical engineering problems.<br />
<br />
''Abstract:''<br />
The talk accessible to nonprofessionals will lead the audience into an exciting journey of the beauty of geometric structures obtained using computational mathematics derived from discontinuous dynamical systems that arise from problems in electrical engineering.<br />
We illustrate how rigorous computational mathematics and elementary number theory is used producing fractal structure of piecewise isometries.<br />
<br />
Key words: fractals, computational mathematics, cyclotomic fields, dynamical systems, digital filters, piecewise isometries, computers producing publishable papers.<br />
<br />
The CV link: http://calculus.sfsu.edu/goetz/vitae.pdf<br />
Arek Goetz is professor of mathematics at San Francisco State University. An active researcher in dynamical systems, software architect and an educator, has delivered over 90 talks on 5 continents. He is a recipient of two National Science Foundation Grants, as well as numerous teaching grants.<br />
<br />
----<br />
<br />
=== Thursday, September 11th, at 4:00pm in BK207 ===<br />
<br />
''Speaker:'' Giovanni Sambin<br />
Department of Pure and Applied Logic<br />
University of Padua<br />
<br />
''Title:''<br />
The Basic Picture: an interactive introduction by questions & answers.<br />
<br />
''Abstract:''<br />
To define a topology on a set $X$ in a constructive way (where contructive here means both intuitionistic and predicative), one needs a second set $S$ and a family of subsets of $X$ indexed on $S$, that is, a relation between $X$ and $S$. I have called this structure a basic pair.<br />
One can show that interior and closure of a subset are defined in a basic pair by formulae which are strictly dual of each other (the former is of the form $\exists\forall$, the latter $\forall \exists $).<br />
<br />
Continuity between basic pairs is expressed by a commutative diagram of relations (up to a suitable notion of equality).<br />
<br />
The main pointfree structure has a primitive for closed subsets (positivity) which is dual to that for open subsets (formal cover), and they are linked by a condition (called compatibility) which is best expressed by using the notion of overlap between subsets (the existential dual of inclusion).<br />
<br />
These discoveries show that there is a clear and simple structure underlying topology, and that it is a sort of applied logic. I have called it the Basic Picture. Both traditional ("pointwise") and pointfree topology in the proper sense are obtained as a special case. In fact, a topological space is just a basic pair equipped with convergence (any two approximations of a point can be refined to a third), and continuous functions are just those relations which preserve convergence.<br />
<br />
Besides allowing for a fully constructive development of topology, this approach brings to some technical improvements which are new also for the classical approach. In particular, one can prove that the category of topological spaces with continuous relations can be embedded in the category of formal topologies (i.e. pointfree topologies in a constructive sense), thus giving a mathematical form to the well-known claim that pointfree topology generalizes the traditional one with points.<br />
<br />
On all this, I am writing a book (The Basic Picture. Structures for constructive topology", Oxford U.P., forthcoming). After around 20 minutes expanding on the above summary, I am ready to give an introduction to the content and general philosophy of the book, by discussing with the audience any questions they would like to put.<br />
<br />
----<br />
<br />
=== Thursday, August 28, 2008, 4-5 pm, BK 207 ===<br />
''Speaker:'' Dr. Georg Struth (University of Sheffield, UK)<br />
<br />
''Title:'' Verification Based on Algebra and Automated Deduction<br />
<br />
''Abstract:'' The formal analysis and verification of computing systems has so far been dominated by model checkers and other decision procedures which are fully automated, but limited in expressive power, and by interactive theorem provers which are quite expressive, but limited in automation. Due to improved hardware and theoretical developments, automated deduction is currently emerging as a third way in which expressivity and computational power are differently balanced and which conveniently complements the other approaches.<br />
<br />
I will present a new approach to formal verification in which computational algebras are combined with off-the-shelf automated theorem provers for first-order equational logic. The algebras considered are variants of Kleene algebras and their extensions by modal operators. Particular strengths of these structures are syntactic simplicity, wide applicability, concise elegant equational proofs, easy mechanizability and strong decidability.<br />
<br />
I will sketch the axiomatization and calculus of Kleene algebras and modal Kleene algebras, discuss some computationally interesting models, such as traces, graphs, languages and relations, and point out their relationship to popular verification formalisms, including dynamic logic, temporal logic and Hoare logic. I will also report on some automation results in the areas of action system refinement, termination analysis and program verification that demonstrate the benefits and the potential of the algebraic approach.<br />
<br />
----<br />
----<br />
<br />
== Spring 2008 ==<br />
<br />
=== Thursday, May 8, 2008, 1:30-2:30 pm, BK 207 ===<br />
''Speaker:'' Professor Alfonso Cariazzo (University of Sevilla)<br />
<br />
''Title:'' Chen's inequalities in generalized Sasakian-space-forms<br />
<br />
''Abstract:'' Recently, P. Alegre, D. E. Blair and the speaker defined generalized Sasakian-space-forms as those almost contact metric manifolds with a Riemann curvature tensor satisfying the usual equation for a Sasakian-space-form, but with some differentiable functions $f_1; f_2; f_3$ instead of the well-known constant quantities (c + 3)=4 and (c ¡ 1)=4.<br />
In this talk, we will review the main facts about generalized Sasakian-space-forms, such as the existence of interesting examples in any dimension, or the possible structures for these spaces. After that, we will present sharp inequalities involving ±-invariants for submanifolds in this setting, with arbitrary codimension. In fact, ±-invariants, introduced by B.-Y. Chen, have proven to be a key tool in Submanifolds Theory, providing new very useful information concerning the immersion problem.<br />
<br />
----<br />
<br />
=== Thursday, May 1, 2008, 1:30-2:30 pm, BK 207 ===<br />
''Speaker:'' Professor Vincenzo Vespri, (University of Firenze)<br />
<br />
''Title:'' Harnack inequalities for nonlinear parabolic equations<br />
<br />
''Abstract:'' In this talk I'll speak about recent results obtained in collaboration with Emmanuele DiBenedetto and Ugo Gianazza.<br />
In the sixties Moser, using deep Nash ideas, proved Harnack inequalities for nonnegative solutions of linear parabolic equations with $L^\infty$ coefficients. This approach, however, seems not to work in the nonlinear case (for instance in the case of p-Laplacean and porous medium equation). In recent papers published on Calc. Var., Acta Math and Duke Math. J., we give an alternative proof of the Harnack inequality with respect the Moser's one based on DeGiorgi's function classes. This approach is so flexible that it can be extended to the nonlinear case.<br />
<br />
----<br />
<br />
=== Tuesday, April 29, 2008, 1:30-2:30 pm, BK 207 ===<br />
''Speaker:'' Hung-Jen (Steward) Huang, (Chapman University) <br />
<br />
''Title:'' Bayesian Analysis of Errors-in-Variables Growth Curves with Skewness in Models<br />
<br />
''Abstract:'' We propose to analyze model data 1) using errors-in-variables (EIV) model and 2) using the assumptions that the error random variables are subject to the influence of skewness through Bayesian approach. The use of EIV in model is necessary and realistic in studying many statistical problems, but their analysis usually mandate many simplifying and restrictive assumptions. Previous studies have shown the superiority of Bayesian approach in dealing with the complexity of these models. <br />
<br />
In fitting statistical models for the analysis of growth data, many models have been proposed. We selected an extensive list of the most important growth curves and using some of them in our model analysis. Much research using classical approach has clustered on this area. However, the incorporation of EIV into these growth models under Bayesian formulation with skewness models have not yet been considered or studied. A motivating example is presented and in which we expose certain lacunae in the analysis previously done as well as justify, the applicability of the our general approach proposed alone. In addition, auxiliary covariates, both qualitative and quantitative, can be added into our model as an extension. This EIV growth curves with auxiliary covariates in models renders a very general framework for practical application. <br />
<br />
Another illustrative example is also available to demonstrate how Bayesian approach through MCMC (Metropolis Hastings/slice sampling in Gibbs sampler) techniques as well as Bayesian Information Criterion (BIC) for model selection can be utilized in the analysis of this complex EIV growth curves with skewness in models.<br />
<br />
----<br />
<br />
=== Thursday, April 24, 2008, 2:15-3:15 pm, BK 207 ===<br />
''Speaker:'' Alberto Damiano (Chapman University)<br />
<br />
''Title:'' Syzygies, Antisyzygies, and how I defeated the Dirac system in a Singular way<br />
<br />
''Abstract:'' In my talk I will present an overview of some of the results from this year’s collaboration with D. Struppa, and A. and M. Vajiac, together with some of the questions that still remain open. First, I will introduce a new concept of “antisyzygies”, which constitutes a sort of inverse problem within the framework of algebraic analysis. Usually people start from a (non-homogeneous) system of PDEs, and hunt for the integrability conditions. We asked ourselves the opposite question: if we are given the compatibility laws, how can we reconstruct the system in some canonical way? What are the properties of the system that we get? In particular, I will mention the relation between the antisyzygy construction and Hartogs type of phenomena (removability of compact singularities from the solutions).<br />
<br />
On a more computational side, I will present an idea that D. Eelbode and I had during his stay at Chapman. The goal is to construct the syzygies for the Dirac system in several vector variables. I already touched upon some of the possible techniques to computer those syzygies in my previous talks. This time, I will show how to use the computer algebra software Singular and the structure of the super Lie algebra osp(1|2) to get the (minimal) free resolution of the system, in just a few command lines. <br />
<br />
----<br />
<br />
=== Tuesday, April 17, 2008, 1:30-2:30 pm, BK 207 ===<br />
''Speaker:'' Jeff Krause, Shodor Foundation<br />
<br />
''Title:'' Preparing for the Interdisciplinary Challenges of Post-Genomic Biology:<br />
<br />
''Abstract:'' Biology is in a state of flux. The tremendous changes are due to rapidly advancing experimental technologies that are producing previously unheard of quantities of data. Storing these data and extracting information from them have caused an explosion in the field of biomedical informatics. A further quantitative emphasis results from the fact that these new experimental technologies are able to make many measurements from complex multi-scale biological systems in a single experiment. Our ability to effectively validate these data and hypothesize with them is dependent on our ability to produce predictive quantitative models of these systems. While the past decade has been truly exciting for biologists and others drawn to the field, it has resulted in a dire need for curricular reform in the biological sciences in order to prepare students for careers in post-genomic biology. In my talk I will survey the quantitative and computational landscape of contemporary biology, and I will discuss various organizations, programs and resources that have been developed in support of efforts to integrate quantitative and computational training into the undergraduate biology curriculum.<br />
<br />
----<br />
<br />
=== Tuesday, April 8, 2008, 1:30-2:30 pm, BK 207 ===<br />
''Speaker:'' David Eelbode (University of Ghent, Belgium)<br />
<br />
''Title:'' Higher spin operators in Clifford analysis:<br />
<br />
''Abstract:'' In this lecture, we will explain how one can fully exploit the framework of Clifford algebras and Clifford analysis in order to construct a function theory for higher spin Dirac operators. These are to be seen as far-reaching generalizations of the classical Dirac operator, possibly describing (exotic) elementary particles in higher dimensions. We will carefully explain how to describe the underlying invariance with respect to the underlying Lie algebra so(m), and how to relates the associated theory to Clifford analysis in several vector variables.<br />
<br />
This work is done in collaboration with my PhD-student Liesbet Van de Voorde<br />
<br />
----<br />
<br />
=== Thursday, April 3, 2008, 1:30-2:30 pm, BK 207 ===<br />
''Speaker:'' Cyril Rakovski, Department of Preventive Medicine, Division of Biostatistics, Keck School of Medicine, USC<br />
<br />
''Title:'' Novel statistical methods for detecting genetic association between phenotypes and multiple genes:<br />
<br />
''Abstract:'' Association methods employed for finding deleterious mutations in human populations are categorized into two broad classes with respect to the structure of the analyzed data, case-control and family-based. Case-control studies are flexible, powerful and cost-efficient approaches that possess an inherent design disadvantage, susceptibility to inflated rates of false-positive results due to unaccounted population structure and hidden relatedness. Family-based tests for association (FBATs) provide a robust alternative to case-control methods that address the above-mentioned shortcomings by conditioning on the population information. New FBAT extensions for handling multiple correlated genes and a relatedness-adjusted case-control statistical method that accounts for stratified populations are proposed and studied through extensive simulations in various settings. Our results show that in most of the analyzed scenarios the new tests attain higher power than the currently existing approaches.<br />
<br />
----<br />
<br />
=== Thursday, March 6, 2008, 1:30-2:30 pm, BK 207 ===<br />
''Speaker:'' Hendrik de Bie, Ghent University, Belgium<br />
<br />
''Title:'' Harmonic and Clifford analysis in superspace:<br />
<br />
''Abstract:'' Superspaces are spaces with not only commuting variables but also anti-commuting variables. We will show how it is possible to extend harmonic and Clifford analysis to these superspaces by constructing a suitable representation of sl(2) and osp(1|2). Then we will use this representation to consider integration in superspaces and we will give a set of properties that uniquely determine the Berezin integral on the supersphere.<br />
<br />
----<br />
<br />
=== Thursday, February 28, 2008, 1:30-2:30 pm, BK 207 ===<br />
<br />
''Speaker:'' Prof. Peter Jipsen, Chapman University<br />
<br />
''Title:'' Using Gentzen system techniques with existing automated theorem provers and rewriting tools<br />
<br />
''Abstract:'' Gentzen systems have been used to present many logics, such as classical logic, intuitionistic logic, modal logics, substructural logics, and their corresponding algebraic axiomatizations, in modular ways that provide new insights and often lead to effective decision procedures.<br />
The aim of this talk is to show that Gentzen sequent calculi can be used in standard resolution theorem provers to improve their search space characteristics. This is mostly of use with (semi)lattice ordered algebras, and does not require cut-free Gentzen systems. For example it is currently not known if there is a cut-free Gentzen system for residuated Kleene algebras or residuated Kleene lattices. However if axiomatizations for these equational theories are presented in the style of Gentzen sequent rules, then a theorem prover such as Prover9<br />
(www.prover9.org) can be quite an effective reasoning tool in these otherwise rather untractable theories.<br />
I will also discuss how cut-free Gentzen systems can be implemented effectively using standard rewriting tools such as Maude (http://maude.cs.uiuc.edu/).<br />
<br />
----<br />
<br />
=== Thursday, February 21, 2008, 1:30-2:30 pm, BK 207 ===<br />
<br />
''Speaker:'' Prof. Andrew Moshier, Chapman University<br />
<br />
''Title:'' Free Constructions of Directed Complete Partial Orders<br />
<br />
''Abstract:'' We develop a "generators and relations" method of constructing directed complete partial orders (dcpos), and show that the results are indeed free in the usual sense. We then continue by considering the situation where the generator set is equipped with finitary operations, showing that the free construction yields a dcpo algebra (in which the operations are Scott continuous) in the same algebraic variety as the generating structure. We apply the results to the construction of co-products, and the characterization of sub-objects, in the category of "proto-frames". This is joint work with Achim Jung and Steve Vickers of Univ. of Birmingham, UK.<br />
<br />
----<br />
<br />
=== Thursday, February 7, 2008, 1:30-2:30 pm, BK 207 ===<br />
<br />
''Speaker:'' Prof. Jack Stecher, Norwegian School of Economics and Business Administration<br />
<br />
''Title:'' Decision Making and Trade with Subjective Information<br />
<br />
----</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=MathCS_Seminar_2009&diff=15MathCS Seminar 20092021-02-22T18:36:29Z<p>Jipsen: Created page with "== Fall 2009 == The seminar talks are usually in Beckman Hall 207 (corner of [http://maps.google.com/maps?q=N+Glassell+St+%26+University+Dr,+Orange,+CA+92866,+USA&sa=X&oi=ma..."</p>
<hr />
<div>== Fall 2009 ==<br />
<br />
<br />
The seminar talks are usually in Beckman Hall 207 (corner of [http://maps.google.com/maps?q=N+Glassell+St+%26+University+Dr,+Orange,+CA+92866,+USA&sa=X&oi=map&ct=title N. Glassell St and University Drive], Orange, CA 92866)<br />
<br />
<br />
----<br />
=== Thursday, December 3rd, at 4:00pm in VN 116 ===<br />
<br />
''Speaker:'' Prof. Robert Desharnais (CSULB)<br />
<br />
''Title: '' Chaos in a Bottle: Experimental Nonlinear Population Dynamics<br />
<br />
<br />
'' Abstract:'' Research in ecology is increasingly interdisciplinary. This presentation will describe a long-term collaboration among biologists, mathematicians, statisticians which is focused on understanding how nonlinearity manifests itself in the dynamics of ecological populations.<br />
<br />
----<br />
=== Thursday, November 19th, at 5:15pm in VN 116 ===<br />
<br />
''Speaker:'' Prof. Irene Sabadini, Dipartimento di Matematica, Politecnico di Milano<br />
<br />
''Title: '' Slice Hyperholomorphy and its Functional Calculus<br />
<br />
<br />
'' Abstract:'' TBA<br />
<br />
<br />
----<br />
=== Thursday, November 5th, at 4:00pm in VN 116 ===<br />
<br />
''Speakers:'' Prof. Cyril Rakovski and Lisa Brown, Chapman University<br />
<br />
''Title: '' On the ranking of the disease susceptibility locus in family-based candidate gene studies: a simulation-based analysis<br />
<br />
<br />
'' Abstract:'' We carried out an extensive family-based candidate gene simulation study to analyze the position of the true causal single nucleotide polymorphism in the complete list of marker p-values ordered according to their statistical significance. We used the real haplotype structures of 10 genes from the HapMap dataset, various sample sizes that current studies employ and disease models that mimic the characteristics of complex human disorders. We found that the all three factors, gene, disease model and sample size have profound effect on the rank of the causal SNP.<br />
<br />
----<br />
=== Thursday, October 22nd, at 4:00pm in VN 116 ===<br />
<br />
''Speaker:'' Dr. Mihaela Vajiac, Chapman University<br />
<br />
''Title: '' Bicomplex Hyperfunctions<br />
<br />
'' Abstract:'' In this talk we will develop the foundations for a theory of hyperfunctions as cohomology classes of bicomplex hyperholomorphic functions. The sheaf H of bicomplex hyperholomorphic functions was defined and studied in an earlier paper. We discuss some cohomological properties of H, we compute its flabby dimension and we use the knowledge of its resolution to define a sheaf of hyperfunctions. These hyperfunctions will be objects defined on a codimension three real analytic variety in the space BC of hypercomplex numbers. This is consistent with the fact that the flabby dimension of H is three.<br />
<br />
<br />
----<br />
=== Thursday, October 8th, at 4:00pm in VN 116 ===<br />
<br />
''Speaker:'' Dr. Adrian Vajiac, Chapman University<br />
<br />
''Title: '' Singularities of functions of one and several bicomplex variables<br />
<br />
'' Abstract:'' In this talk we introduce the notion of regularity for functions of one, as well as several bicomplex variables.<br />
Moreover, using computational algebra techniques, we prove that regular functions of one bicomplex variable have the property that their compact singularities can be removed.<br />
<br />
<br />
----<br />
=== Thursday, September 17th, at 4:00pm in BK207 ===<br />
<br />
''Speaker:'' Prof. Andrew Moshier, Chapman University<br />
<br />
''Title: '' Concrete Limits of Locales<br />
<br />
'' Abstract:'' In the category of locales, dual to the concrete category of frames, limits are usually constructed as co-limits of frames. In this talk, we reconsider the limit constructions by viewing locales concretely as certain complete meet semi lattices.<br />
<br />
----<br />
=== Thursday, August 27th, at 4:00pm in BK207 ===<br />
<br />
''Speaker:'' Dr. Lev Vaidman, Tel Aviv University<br />
<br />
''Title: '' Where is the Quantum Particle between two Measurements?<br />
<br />
'' Abstract:'' Wheeler Delayed Choice experiment, Elitzur-Vaidman Interaction-free Measurement, and Hosten-Kwiat Counterfactual Computation will be discussed to answer Bohr's forbidden question: "Where is a quantum particle while it is inside a Mach-Zehnder Interferometer?" The analysis reveals a paradoxical feature of a pre- and post-selected quantum particle: it can reach a certain location without being on the path that leads to and from this location.<br />
<br />
----<br />
== Spring 2009 ==<br />
<br />
<br />
=== Thursday, March 5th, at 4:00pm in BK207 ===<br />
<br />
''Speaker:'' Dr. Peter Jipsen, Chapman University<br />
<br />
''Title:''<br />
Topological duality, canonical extensions and decidability for lattices with quasioperators.<br />
<br />
''Abstract:''<br />
Lattice-ordered monoids, residuated lattices, modal lattices and De Morgan lattices are all examples of lattices with quasioperators, i.e. operations that preserve joins or send meets to joins in each argument or preserve meets or send joins to meets in each argument. In a previous seminar talk Prof. Moshier presented a duality between bounded lattices and a natural subcategory of topological spaces. We will review this duality and extend it to bounded lattices with quasioperators. We consider the connection to earlier dualities of Urquhart, Hartung, and Hartonas and to the canonical extension by Gehrke and Harding, as well as to Galois frames with additional relations.<br />
<br />
Within this framework, we then discuss techniques for proving the decidability of the equational theory of various varieties of bounded lattices with quasioperators. We will also consider algorithms for constructing finite models in these varieties, and present an implementation that enumerates all models based on a given finite Galois frame. <br />
<br />
----<br />
<br />
=== Thursday, February 19th, at 4:00pm in BK207 ===<br />
<br />
''Speaker:'' Professor Bernhard Banaschewski<br />
<br />
''Title:''<br />
Point-free Topology and the Representation of Lattice-ordered Rings<br />
<br />
''Abstract:''<br />
The classical representation of archimedian f-rings with unit by continuous functions on topological spaces unavoidably requires the use of extended realvalued functions, with all the inherent complications that involves. By way of contrast, the natural counterpart of the usual notion of a real-valued continuous function in point-free topology provides a setting in which these l-rings can be embedded in the corresponding rings of real-valued continuous functions. This talk will describe that point-free representation in terms of the relevant function ring functor and its left adjoint, and then show how this adjointness may be used to obtain certain results about f-rings from point-free topology.<br />
<br />
This seminar is part of CHAPMAN UNIVERSITY's "WORKSHOP ON POINT-FREE TOPOLOGY" to which you are also invited.<br />
Week of: February 17–20, 2009<br />
<br />
----<br />
<br />
=== Week of February 16th-20th, in BK207 ===<br />
<br />
''WORKSHOP ON POINT-FREE TOPOLOGY'' in honor of Bernhard Banaschewski’s visit to ChapmanvUniversity.<br />
<br />
Organized by Dr. Andrew Moshier<br />
<br />
''Initial schedule:''<br />
Feb 17 <br />
<br />
11:00 – 1:00 B. Banaschewski<br />
Essential Completion in Point-free Topology, Part I.<br />
<br />
4:00 – 5:00 M. A. Moshier<br />
Skew frames and Point-free Bitopology.<br />
<br />
Feb 18 <br />
<br />
11:00 – 1:00 B. Banaschewski<br />
Essential Completion in Point-free Topology, Part II.<br />
<br />
Feb 19 <br />
<br />
10:00 – 11:15 F. Dashiell<br />
Kuratowski Reduction in ?-frames.<br />
<br />
4:00 – 5:00 B. Banaschewski<br />
Point-free Topology and the Representation of Lattice-ordered Rings.<br />
<br />
Feb 20 <br />
<br />
11:00 – 1:00 B. Banaschewski<br />
Essential Completion in Point-free Topology, Part III.<br />
<br />
For more information and updates contact:<br />
M. Andrew Moshier<br />
(714) 997 6628<br />
<br />
----<br />
<br />
=== Thursday, February 12th, at 4:00pm in BK207 ===<br />
<br />
''Speaker:'' Dr. Andrew Moshier Chapman University<br />
<br />
''Title:''<br />
Topological Duals and Canonical Extensions for Arbitrary Bounded Lattices<br />
<br />
''Abstract:''<br />
Is there a subcategory of Top (the category of topological spaces) that is dually equivalent to BLat (the category of bounded lattices)?<br />
<br />
This question has only been affirmatively answered either by restricting BLat to special cases, e.g., Boolean or distributice lattices, or by expanding Top to a category of spaces with extra structure. The latter approach indeed yields duality theories for the general case of BLat, but the results are highly technical and have turned out not to be particularly useful to lattice theorists.<br />
<br />
We give an affirmative answer to the above question with no qualifications. <br />
The result is a significant improvement in the theory of topological duality for lattices. To illustrate the point, we show that the canonical extension of a lattice 'lives' inside its topological dual in a very natural way. <br />
Time permitting, as a further illustration, we will also derive a representation theory for orthocomplemented lattices from the general setting.<br />
<br />
----<br />
<br />
=== Friday, January 12th, at 1:00pm in BK207 ===<br />
<br />
''Speaker:'' Dr. Rebecca Goldin, GMU, Director of Research at STATS (www.stats.org), a nonprofit affiliated with GMU.<br />
<br />
''Title:''<br />
The Two-Sphere Spinning Around an Axis: an Introduction to Symplectic Geometry with Hamiltonian Group Actions<br />
<br />
''Abstract:''<br />
I will describe a beautiful relationship between symplectic manifolds with Hamiltonian group actions, and convex polytopes. The essential goal in this "business" is to find a way of describing difficult geometry in terms of combinatorial objects such as polytopes. We will illustrate these ideas through one of the most basic example, the two-sphere with a circle rotating it around an axis. All terms will be defined.</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=MathCS_Seminar_2010&diff=14MathCS Seminar 20102021-02-22T18:35:44Z<p>Jipsen: Created page with "== Fall 2010 == The seminar talks are in Von Neumann Hall 116 (545 W Palm Ave corner of W Palm Ave and railroad, Orange, CA 92866) The talks usually start at 4 pm. From 3:30..."</p>
<hr />
<div>== Fall 2010 ==<br />
<br />
The seminar talks are in Von Neumann Hall 116 (545 W Palm Ave corner of W Palm Ave and railroad, Orange, CA 92866)<br />
<br />
The talks usually start at 4 pm. From 3:30 pm to 4:00 pm is time for refreshments and interesting conversations with the speaker, so consider coming a bit early.<br />
<br />
<br />
<br />
----<br />
<br />
=== Thursday, December 9, at 3:30 pm in VN 116 ===<br />
<br />
''Speaker:'' Prof. M. Andrew Moshier (Chapman University)<br />
<br />
''Title:'' A Bitopological Point-free Approach to Compactifications<br />
<br />
''Abstract:'' D-frames, consist of a pair of frames, together with two relations which serve as abstractions of disjointness and covering, are a suitable point-free counterpart to bitopological spaces. In particular, the "topological" separation axioms of regularity and normality have natural analogues in d-frames. We develop a bitopological point-free notion of complete regularity and characterise all compactifications of completely regular d-frames. Given that normality of topological spaces does not behave well with respect to products and subspaces, probably the most surprising result is this: The compact regular coreflection of completely regular d-frames (Stone-C(ech compactification) factors through the subcategory of normal d-frames. Moreover, any compactification can be obtained by first producing a regular normal d-frame and then applying the Stone-C(ech compactification to it. Our point-free bitopological compactification subsumes all classical compactifications of frames as well as Smyth?s stable compactification.<br />
<br />
This is joint work with Olaf Klinke and Achim Jung (Univ. of Birmingham, UK).<br />
<br />
<br />
<br />
----<br />
<br />
=== Thursday, November 18, at 4 pm in VN 116 ===<br />
<br />
''Speaker:'' Prof. John Harding (New Mexico State University)<br />
<br />
''Title:'' Subalgebras of orthomodular lattices<br />
<br />
''Abstract:'' Recent approaches to the foundations of quantum mechanics initiated by Isham and others make use of the topology determined by the abelian subalgebras of a von Neumann algebra to treat various quantum mechanical concepts as sheafs of structures that locally behave as the classical counterparts. This leads to our investigation of properties of the poset of abelian subalgebras of a von Neumann algebra, or more generally, of the poset of Boolean subalgebras of an orthomodular lattice. <br />
<br />
<br />
<br />
----<br />
<br />
=== Tuesday, November 9, at 4 pm in VN 116 ===<br />
<br />
''Speaker:'' Fabrizio Colombo, Politecnico of Milano<br />
<br />
''Title:'' An introduction to the F-functional calculus<br />
<br />
''Abstract:'' In this talk, I will recall the classical Fueter mapping theorem and I will show how to provide a new version of the result written in integral form. <br />
I will use this integral representation to construct a functional calculus for n-tuples commuting operators using a subclass of monogenic functions.<br />
<br />
<br />
<br />
''Speaker:'' Irene Sabadini, Politecnico of Milano<br />
<br />
''Title:'' Some new results on the Dirac complex<br />
<br />
''Abstract:'' The complex of several Cauchy-Fueter operators is nowadays quite well understood and its knowledge implies several analytical consequences on the space of regular functions with quaternionic values. The higher dimensional analogue, i.e. the complex of several Dirac operators, is known in the case of three operators in the so-called "radial case". We will show how to prove that the radial case is in fact the general case, using commutative algebra techniques.<br />
<br />
<br />
<br />
----<br />
<br />
=== Thursday, September 30, at 4 pm in VN 116 ===<br />
<br />
''Speaker:'' Prof. Daniele Struppa (Chapman University)<br />
<br />
''Title:'' The mathematical legacy of Leon Ehrenpreis: 1930 - 2010<br />
<br />
''Abstract:'' Leon Ehrenpreis was one of the greatest Fourier analysts<br />
of the twentieth century. In this talk I will discuss his celebrated Fundamental Principle, and its implications for contemporary research, including some recent results of mine on approximate solutions of differential equations.<br />
<br />
<br />
<br />
----<br />
<br />
=== Thursday, September 16, at 4 pm in VN 116 ===<br />
<br />
''Speaker:'' Dr. Peter Jipsen (Chapman University)<br />
<br />
''Title:'' Relation algebras as residuated lattices expanded with a De Morgan negation<br />
<br />
''Abstract:'' In this talk we consider the variety DmRL' of residuated lattices with a unary De Morgan operation '. It has the same signature as relation algebras and includes a subvariety qRA of quasi-relation algebras defined by adding equations that ensure ' is a homomorphism from the residuated lattice to its dual. We show how relation algebras are a natural subvariety of qRA, but that qRA has the distinct advantage of having a decidable equational theory. This type of result is only possible if the order structure of relation algebras is generalized to De Morgan lattices, since Kuruczs, Nemeti, Sain and Simon proved in 1993 that any `large enough' variety with Boolean algebra reducts and with an associative operator has an undecidable equational theory.<br />
We also extend a result of Jonsson and Tsinakis [1993], where relation algebras are shown to be term-equivalent to a subvariety of residuated Boolean monoids, to the more general setting of quasi relation algebras. Much of the work reported here was done in collaboration with Nikolaos Galatos.<br />
<br />
<br />
<br />
----<br />
<br />
=== Thursday, September 9, at 4 pm in VN 116 ===<br />
<br />
''Speaker:'' Dr. Mihaela Vajiac (Chapman University)<br />
<br />
''Title:'' The notion of Holomorphicity in the context of Multicomplex Spaces<br />
<br />
''Abstract:'' In this presentation we study regularity notions and properties of functions defined on multicomplex spaces BC_n. Our results constitute a generalization of our previous research in this field (joint work with D.C. Struppa and A. Vajiac).<br />
<br />
<br />
<br />
----<br />
<br />
<br />
== Summer 2010 ==<br />
<br />
<br />
=== Thursday, July 22nd, at 10:00am in VN116 ===<br />
<br />
''Speaker:'' Dr. Dan Zaffran, KEIST (South Korea)<br />
<br />
''Title:'' Euler's formula and (much) more<br />
<br />
'' Abstract:'' A cube has F=6 faces, E=12 edges and V=8 vertices. A pyramid with a square base has F=5 faces, E=8 edges and V=5 vertices. Euler discovered in 1750 that for these two cases, or for any other polyhedron, F-E+V=2. He published the result, but he confessed that he was not able to prove it. This celebrated "Euler's formula" is the starting point of many results and conjectures in higher dimensions. I will explain some of them, and focus on the surprising methods that have been used to solve these problems: topological manifolds and their algebraic topology, algebraic geometry...<br />
<br />
<br />
----<br />
<br />
== Spring 2010 ==<br />
<br />
The seminar talks are usually in Von Neumann Hall 116 (545 W Palm Ave corner of W Palm Ave and railroad, Orange, CA 92866)<br />
<br />
<br />
<br />
----<br />
<br />
=== Tuesday, May 11th, at 4:30pm in VN116 ===<br />
<br />
''Speaker:'' Dr. Ali Nayeri,, Chapman University<br />
<br />
''Title: '' The State of the Universe: Certain Present, Dark Future and Shady Past<br />
<br />
'' Abstract:'' The past 20 years have seen dramatic advances in our understanding about the universe. We seem to have established the basic parameters describing the behavior of our expanding Universe, thereby putting cosmology on a firm empirical footing. But the emerging standard? model of the universe leaves many details to be worked out, and new ideas are emerging that challenge the theoretical framework on which the structure of the Big Bang is based. There is still a great deal left to explore in cosmology.<br />
<br />
In this talk I will first review the status of the universe as we (think) we understand now. After reviewing the standard model of cosmology and the problems within I will present the new idea of structure formation and avoiding the initial singularity based on string theory which was developed in Harvard recently by my colleagues and I.<br />
<br />
<br />
<br />
----<br />
<br />
=== Thursday, May 6th, at 4:00pm in VN116 ===<br />
<br />
''Speaker:'' Dr. Boyana Norris, Argonne National Laboratory, Mathematics and Computer Science Division<br />
<br />
''Title: '' Annotation-Based Empirical Performance Tuning of Scientific Applications<br />
<br />
'' Abstract:'' In many high-performance scientific applications, computational scientists spend significant time tuning codes for a particular high-performance architecture. Tuning approaches range from the relatively nonintrusive (e.g., by using compiler options) to extensive code modifications that attempt to exploit specific architecture features. Intrusive techniques often result in code changes that are not easily reversible, which can negatively impact readability, maintainability, and performance on different architectures. We describe an extensible annotation-based empirical tuning system called Orio, which is aimed at improving both performance and productivity by enabling scientific software developers to insert annotations in the form of structured comments that trigger a number of low-level performance optimizations on a specified code fragment. To maximize the performance tuning opportunities, we have designed the Orio framework to support both architecture-independent and architecture-specific code optimizations. Given the annotated code as input, Orio generates many tuned versions of the same operation and empirically evaluates the versions to select the best performing one for production use. We have also integrated other, independently developed, transformation approaches into Orio, such as the Pluto automatic parallelization tool for generation of efficient OpenMP-based parallel code and the PrimeTile tool for parametrized tiling of imperfect loop nests. We describe experimental results involving a number of computational kernels, including dense array and sparse matrix operations.<br />
<br />
<br />
----<br />
<br />
=== Thursday, April 22nd, at 3:00pm in VN116 ===<br />
<br />
''Speaker:'' Dr. Zair Ibragimov, Cal State Fullerton<br />
<br />
''Title: '' Hyperbolization of metric spaces<br />
<br />
'' Abstract:'' Suppose Z is a locally compact noncomplete metric space. We introduce a metric u_Z on Z, which induces the topology of Z and turns Z into a hyperbolic metric (in the sense of Gromov). The metric u_Z can be thought of as a canonical Gromov hyperbolic metric of Z since it appears that many Gromov hyperbolic metrics introduced in geometric function theory (such as: the Poincare metric, Barbilian metric, the hyperbolic cone metric, the j-metric and the hyperbolic metric of the hyperspaces) are special cases of u_Z (up to a quasiisometry). In particular, this in combination with the Gromov hyperbolicity of u_Z gives alternative proofs of the Gromov hyperbolicity of these metrics.<br />
<br />
<br />
<br />
<br />
----<br />
<br />
=== Thursday, April 15th, at 3:00pm in VN116 ===<br />
<br />
''Speaker:'' Dr. David Porter, Professor of Economics and Mathematics, Chapman University<br />
<br />
''Title: '' Combinatorial Auctions (with Stephen Rassenti)<br />
<br />
'' Abstract:'' A combinatorial auction is a resource allocation process that can be<br />
implemented when multiple resources must be simultaneously allocated<br />
amongst competing users, and information concerning the values of the<br />
various possible uses and constraints affecting those uses is<br />
decentralized. We will go through the design and implementation of<br />
various methods for solving this problem and the computational and<br />
incentive issues involved in such designs. <br />
<br />
<br />
----<br />
<br />
=== Tuesday, April 6th, at 3:00pm in VN116 ===<br />
<br />
''Speaker:'' Prof. Le Hung Son, Hanoi University of Technology, Vietnam<br />
<br />
''Title: ''Additive Cousin Problem and Hartogs Extension Theorem in Clifford and Quaternion Analysis<br />
<br />
'' Abstract:'' It is known that the Additive Cousin Problem and Hartogs Extension Theorem are the fundamental events in Complex Analysis of several variables. The first one allows the construction of the global meromorphic functions by given local singularities and the second one states that holomorphic functions of several complex variables possess non isolated singularities. This talk deals with some remarks and comments concerning the same problems in Clifford Analysis, Quaternion Analysis and the theory of functions taking value in a Matrix Algebra.<br />
Furthermore in this talk we will try to reflect some new ideas and results on Clifford and Quaternion Analysis of higher dimensions and their applications to Partial Differential Equations, Mathematical Physics and Engineering Problems.<br />
<br />
----<br />
<br />
=== Thursday, March 25th, at 3:00pm in VN116 ===<br />
<br />
''Speaker:'' Dr. Hendrik De Bie, Belgium and Oregon State<br />
<br />
''Title: ''The Clifford-Fourier transform<br />
<br />
'' Abstract:'' The Clifford-Fourier transform has been introduced a couple of years <br />
ago by Brackx et al. So far, it is probably the most interesting <br />
attempt at introducing a Fourier transform in the setting of Clifford <br />
analysis, because it is defined by a similar exponential operator as <br />
the classical Fourier transform. However, several questions regarding <br />
this transform are still open: the integral kernel is not known, it is <br />
not known on which function spaces the transform is defined, there is <br />
only a formal proof of the inversion formula, etc.<br />
<br />
In recent work with Yuan Xu, I have succeeded in answering most of <br />
these questions. We have found explicit expressions for the kernel in <br />
all even dimensions, leading to estimates of the transform. We have <br />
introduced a generalized translation operator and a related <br />
convolution structure, which can be used to prove the inverse of the <br />
transform.<br />
<br />
In this talk, I first give an overview of the classical Fourier <br />
transform and how it can be generalized to the Clifford-Fourier <br />
transform (stressing the Lie algebraic background). Next, I will <br />
explain our recent results.<br />
<br />
[No special knowledge of Clifford analysis is necessary to follow the talk]<br />
<br />
----<br />
<br />
=== Thursday, March 18th, at 3:00pm in VN116 ===<br />
<br />
''Speaker:'' Dr. Peter Jipsen, Chapman University<br />
<br />
''Title: '' Periodic lattice-ordered pre-groups are distributive<br />
<br />
'' Abstract:'' \emph{Pregroups} are algebras of the form<br />
$(A,\cdot,1,^l,^r,\le)$<br />
such that $(A,\le)$ is a poset, $(A,\cdot,1)$ is a monoid, $x\le<br />
y\Rightarrow uxv\le uyv$,<br />
and $^l,^r$ are two unary operations, called the \emph{left and<br />
right adjoint} that satisfy<br />
$$<br />
x^l\cdot x\le1\le x\cdot x^l\qquad x\cdot x^r\le1\le x^r\cdot x.<br />
$$<br />
They were defined by J.~Lambek in 1999 in a paper that provides a<br />
new approach to categorial grammars, and they have been studied in<br />
a series of recent papers by W.~Buszkowski from an algebraic and<br />
proof theoretic perspective. Pregroups give an abstract setting for<br />
studying maps on a poset that have all iterated left and right adjoints<br />
(i.e. all residuals and dual residuals). E.g. partially ordered groups,<br />
and hence groups, are pregroups. A \emph{lattice-ordered pregroup}<br />
or $\ell$-pregroup is a pregroup expanded with $\wedge,\vee$ such<br />
that the underlying poset is a lattice with respect to these operations.<br />
The variety of $\ell$-pregroups contains all $\ell$-groups and is<br />
itself contained in the variety of involutive residuated lattices.<br />
An $\ell$-pregroup is \emph{periodic} if it satisfies the identity<br />
$x^{ll\ldots l}=x$ for some finite iteration of left adjoints. In<br />
this talk it is proved that all such $\ell$-pregroups have distributive<br />
lattice reducts. The proof was found with assistance from the equational<br />
theorem prover Waldmeister. It is still an open problem whether the<br />
same result holds for all $\ell$-pregroups. <br />
<br />
----<br />
<br />
=== Thursday, February 26th, at 4:00pm in VN116 ===<br />
<br />
''Speaker:'' Dr. Marina Borovikova, CSUF<br />
<br />
''Title: '' Symmetric products of lines and circles.<br />
<br />
'' Abstract:'' The notion of symmetric product of topological spaces was introduced in 1931 by two Polish mathematicians, Karol Borsuk and Stanislaw Ulam. Since then it has been studied by many authors, mostly in topology. Recently, Z. Ibragimov has initiated the study of the symmetric product of metric spaces from a point of view of geometric function theory. Given a metric space $X$ and $n\geq 2$, the $n^{th}$ symmetric product $X$ is the set of all subsets of $X$ of cardinality less or equal to $n$, equipped with the Hausdorff metric. In this talk, I will discuss some results of K. Borsuk, S. Ulam and R. Bott on the $3^{rd}$ symmetric product of the real line $\mathbb R$ and the unit circle $\mathbb S^1$, and present some new results. (Joint work with Z. Ibragimov).<br />
<br />
<br />
----<br />
=== Thursday, February 18th, at 4:00pm in VN116 ===<br />
<br />
''Speaker:'' Dr. Oscar Villareal, UCI<br />
<br />
''Title: '' Rational points on commutative algebraic groups and the Zilber-Pink conjecture.<br />
<br />
'' Abstract:'' Let $A$ be an semiabelian variety and $X$ a subvariety.<br />
The Zilber-Pink conjecture states that the intersection of $X$ with<br />
all of the semiabelian subvarieties of $A$ of codimension greater than<br />
the dimension of $X$ is not Zariski dense. We give some of the<br />
motivation behind this conjecture along with known results.<br />
<br />
<br />
----<br />
=== Thursday, February 11th, at 4:00pm in VN116 ===<br />
<br />
''Speaker:'' Oepomo, Tedja (WLAC)<br />
<br />
''Title: '' Survey of power, QR, and Oepomo's iterative methods for solution of largest eigenvalue of essentially positive matrices.<br />
<br />
'' Abstract:'' Many of the popular methods for the solution of largest eigenvalue of essentially positive irreducible matrices are surveyed with the hope of finding an efficient method suitable for electromagnetic engineering, radiation problems, system identification problems, and solid mechanics. Eigenvalue computations are both fundamental and ubiquitous in computational science and its fast application areas. Some comparisons between several known algorithms, i.e. Power and QR methods, and earlier theory of Oepomo iterative techniques for solving largest eigenvalue of nonnegative irreducible matrices are presented since there is a continuing demand for new algorithm and library software that efficiently utilize and adapt to new applications.<br />
<br />
<br />
----<br />
=== Thursday, January 28th, at 4:00pm in VN116 ===<br />
<br />
''Speaker:'' Prof. Jaroslaw Harezlak, Indiana University School of Medicine<br />
<br />
''Title: '' Impact of the design matrix structure on the performance of LASSO: An empirical study<br />
<br />
'' Abstract:'' High-throughput technologies in medical research provided statisticians with an ever increasing amounts of data. One of the methodological and practical challenges in the analysis of such data is variable selection in regression models. The past 15 years brought a formidable number of methods dealing with the variable selection in the case when the number of covariates is much larger than the number of observations (p >> n). Majority of the methods fall under the category of penalized likelihood which includes ridge regression, LASSO and its variations, SCAD and Dantzig selector.<br />
<br />
In our work, we provide simulation results on the performance of LASSO in the case of strong dependence between the columns of the design matrix X. We consider the estimation error, prediction error and a measure of concordance between the true and selected variables. We study the dependence of the results on the design matrix specification, “irrepresentability condition” of Zhao and Yu (2006) and "phase transition" of Donoho and Stodden (2006). We also compare these results with the more common situation of orthogonality of columns of X.<br />
<br />
In the compound symmetry case, we find that the increased dependence between the columns of X results in larger estimation error, but decreased prediction error. In the anisotropic correlation case, both estimation and prediction errors are the largest when the covariates exhibit both positive and negative correlations.<br />
<br />
<br />
----<br />
=== Monday, January 4th to Saturday, January 15th in VN116 ===<br />
<br />
''Workshop:'' OCCTAL WORKSHOP ON CONTEMPORARY TOPOLOGY<br />
<br />
<br />
''Speaker:'' Prof. Bernhard Banaschewski, McMaster University <br />
<br />
''Title: '' Essential completions in categories of Archimedean l-groups with order unit<br />
<br />
<br />
''Speaker:'' Prof. Bernhard Banaschewski, McMaster University <br />
<br />
''Title: '' On the ccc characterization of the function rings in pointfree topology.<br />
<br />
<br />
''Speakers:'' Prof. Rick Ball, University of Denver, and Dr. Joanne Walters-Wayland, OCCTAL<br />
<br />
''Title: '' The K-Briar Patch<br />
<br />
<br />
''Speaker:'' Dr. Peter Jipsen, Chapman University<br />
<br />
''Title: '' Some open problems regarding lattice-ordered pre-groups<br />
<br />
<br />
''Speaker:'' Prof. M. Andrew Moshier, Chapman University<br />
<br />
''Title: '' Locales and Quantales Concretely<br />
<br />
<br />
----</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=MathCS_Seminar_2011&diff=13MathCS Seminar 20112021-02-22T18:35:09Z<p>Jipsen: Created page with "''Seminar Organizers:'' Peter Jipsen and Cyril Rakovski == Fall 2011 == === Thursday, December 8 at 4:00 pm in VN 116 === ''Speaker:'' '''Professor Yakir Aharonov, [http:/..."</p>
<hr />
<div>''Seminar Organizers:'' Peter Jipsen and Cyril Rakovski<br />
<br />
== Fall 2011 ==<br />
<br />
<br />
=== Thursday, December 8 at 4:00 pm in VN 116 ===<br />
<br />
''Speaker:'' '''Professor Yakir Aharonov, [http://www.chapman.edu Chapman University] and [http://www.chapman.edu/ACFS/Quantum/default.asp Center of Excellence in Quantum Studies]'''<br />
<br />
''Title:'' '''Weak measurements and the discovery of a new kind of mathematics called superoscillations'''<br />
<br />
''Abstract:'' We are taught that if waves with a variety of wavelengths are superposed, then we cannot create structures whose details are smaller than the shortest wavelength in the original superposition. But this is not correct. That is, even if the smallest wave has a wavelength of 1m, we can create arbitrarily detailed structures, say, with feature sizes of 1mm.<br />
<br />
This miracle comes with a penalty: outside the superoscillatory region, the wave must be exponentially large. As an example, suppose we wanted to reproduce a Beethoven symphony with sound frequencies not larger than 1Hz, then somebody (possibly far away) would have to listen to sounds exp(10^19) louder.<br />
<br />
The new kind of mathematics we’ve been developing here at Chapman (a/k/a Superoscillations) has had significant implications for signal processing and has led to new kinds of microscopes which can resolve sub-wavelength structures without the use of evanescent waves.<br />
<br />
We were led to this discovery as a result of our work in quantum mechanics concerning the relationship between past, present and future and weak measurements.<br />
<br />
In this talk I will describe how this came about along with some new exciting discoveries concerning the nature of superoscillations.<br />
<br />
'''[http://mathcs.chapman.edu/~jipsen/seminarposters/Aharonov_120811.pdf Poster]'''<br />
<br />
<br />
----<br />
<br />
<br />
=== Thursday, December 8 at 12:00 noon in VN 116 ===<br />
<br />
''Speaker:'' '''Dr. Joanne Walters-Wayland, [http://mathcs.chapman.edu/CECAT/ Chapman University Center of Excellence in Computation, Algebra and Topology (CECAT)]'''<br />
<br />
''Title:'' '''The wizard of Coz'''<br />
<br />
''Abstract:'' The importance of considering topologies and topological properties via real-valued functions is indisputable – the well-known book by Gillman and Jerison, Rings of Continuous Functions, more than substantiates this claim. In a pointfree setting, this becomes, in my opinion, even more obvious. I shall endeavor to explain my fascination with the cozero part of a frame. By illustrating various aspects of “Coz”, highlighting a few of my favorite properties and explaining some of the problems I am attempting to understand, I hope to convey to the audience, albeit in a small and somewhat superficial way, why "Coz" is so magical and alluring.<br />
<br />
'''[http://mathcs.chapman.edu/~jipsen/seminarposters/Walters-Wayland_120811.pdf Poster]'''<br />
<br />
<br />
----<br />
<br />
<br />
=== Friday, November 18 at 3:00 pm in VN 116 ===<br />
<br />
'''First [http://www.chapman.edu Chapman University] and [http://www.csuf.edu Cal State University Fullerton] joint Mathematics Colloquium'''<br />
<br />
'''Program'''<br />
<br />
'''Dr. Bogdan Suceava (CSUF)''' – 3:00 - 3:20<br><br />
''Title:'' A question of David Hilbert and its application to classes of metrics<br />
<br />
'''Lucy Odom (CSUF Undergraduate)''' – 3:25 - 3:45<br><br />
''Title:'' Chasles Angle Invariance Property for the Helicoid<br />
<br />
'''Peter T. Ho (CSUF Undergraduate)''' – 3:50 - 4:10<br><br />
''Title:'' Rotation Hypersurfaces in Lorentz-Minkowski Space with All Points Umbilics<br />
<br />
'''Dr. Peter Jipsen (Chapman)''' – 4:15 - 4:35<br><br />
''Title:'' Computational Investigations of the Lattice of Lattice Varieties<br />
<br />
'''[http://mathcs.chapman.edu/~jipsen/seminarposters/CSF_joint_colloquium.pdf Poster]'''<br />
<br />
<br />
----<br />
<br />
<br />
=== Thursday, November 17 at 4:00 pm in VN 116 ===<br />
<br />
''Speaker:'' '''Robert Campbell, [http://www.uci.edu University of California at Irvine]'''<br />
<br />
''Title:'' '''Interplanetary Communication Made Possible With Algebraic Coding'''<br />
<br />
''Abstract:'' What does it take to send a message across our solar system? Moreover, if I have trouble maintaining a connection on my cell phone calls how does NASA plan to communicate with its satellites in deep space? Algebraic Coding to the rescue! Combining the power of computer science with the theory of mathematics we can create messages that fix themselves when an error occurs.<br />
<br />
'''[http://mathcs.chapman.edu/~jipsen/seminarposters/Campbell_MathCS_seminar.pdf Poster]'''<br />
<br />
<br />
----<br />
<br />
<br />
=== Thursday, November 3 at 4:00 pm in VN 116 ===<br />
<br />
''Speaker:'' '''Monroe Eskew, [http://www.uci.edu University of California at Irvine]'''<br />
<br />
''Title:'' '''Definability and Infinity'''<br />
<br />
''Abstract:'' What does it mean for a collection to be finite? On the one hand, we have our preschool notion that a collection is finite when it can be counted with natural numbers in a way that terminates. On the other hand, there is a definition due to Dedekind that a set is finite if and only if it cannot be put in one-to-one correspondence with a proper subset. Intuitively these two notions should be equivalent, but can we prove it? I will argue that to avoid a circular argument, one direction requires more care than one would initially think. Further, the other direction is true only by virtue of the Axiom of Choice. To outline the proof of this fact, we will examine formal notions of definiabilty and the set-theoretic technique of forcing.<br />
<br />
'''[http://mathcs.chapman.edu/~jipsen/seminarposters/Eskew_111030.pdf Poster]'''<br />
<br />
<br />
----<br />
<br />
<br />
=== Thursday, October 6 at 3:00 pm in VN 116 ===<br />
<br />
''Speaker:'' '''Dr. Fred Dashiell, [http://www.ucla.edu UCLA] and [http://mathcs.chapman.edu/CECAT/ Center of Excellence in Computation, Algebra and Topology (CECAT)]'''<br />
<br />
''Title:'' '''Various descriptions of hyperstonian Boolean Algebras'''<br />
<br />
''Abstract:'' The study of von Neumann algebras in the late 1940’s led Dixmier to identify the class of compact Hausdorff spaces L which occur when C(L) is a Banach dual space. Dixmier called these spaces “hyperstonian”, and they are totally disconnected, therefore they also represent certain Boolean algebras, which for the purposes of this talk I also call hyperstonian Boolean algebras. These Boolean algebras are complete as lattices, and obey a further condition as to the existence of certain measures on them. Every compact space has a unique “hyperstonian cover”, and this dualizes to the existence of a hyperstonian extension of every Boolean algebra. This talk discusses two approaches to an algebraic description of the hyperstonian cover.<br />
<br />
'''[http://mathcs.chapman.edu/~jipsen/seminarposters/Dashiell.pdf Poster]'''<br />
<br />
<br />
----<br />
<br />
<br />
=== Thursday, September 29 at 3:00 pm in VN 116 ===<br />
<br />
''Speaker:'' '''Dr. Peter Jipsen, [http://www.chapman.edu Chapman University] and [http://mathcs.chapman.edu/CECAT/ Center of Excellence in Computation, Algebra and Topology (CECAT)]'''<br />
<br />
''Title:'' '''The finite congruence lattice representation problem in universal algebra'''<br />
<br />
''Abstract:'' The central problem of this talk asks which finite lattices are congruence lattices of finite algebras. I will give all necessary background and show pictures of congruence lattices of small unary algebras. The problem is still open after 50 years, but recently, in collaboration with W. DeMeo, R. Freese, B. Lampe and J.B. Nation at the University of Hawaii, we have shown that all 7-element lattices, except possibly one of them, are congruence lattices of finite algebras. Students can make progress on this problem by searching for finite algebras with specific congruence lattices (either "by hand" or by doing some programming). I will also demonstrate Ralph Freese's Universal Algebra Calculator (uacalc.org) which makes it possible to easily calculate and display congruence lattices of small algebras.<br />
<br />
<br />
----<br />
<br />
<br />
=== Thursday, September 22 at 3:00 pm in VN 116 ===<br />
<br />
''Speaker:'' '''Professor M. Andrew Moshier, [http://www.chapman.edu Chapman University] and [http://mathcs.chapman.edu/CECAT/ Center of Excellence in Computation, Algebra and Topology (CECAT)]<br />
<br />
''Title:'' '''Point-free duality for Archimedean l-groups with strong order unit'''<br />
<br />
''Abstract:'' Classically, archimedean lattice ordered groups (l-groups) with strong order unit are representable as sub-l-groups of continuous real functions on compact regular spaces. This fact, however, hinges on understanding the real numbers non-constructively. For that matter, even the proof that archimedean l-groups are commutative is not trivial (without the aid of the representation theorem). <br />
<br />
We establish an analogous representation of archimedean l-groups with strong order unit in a category of continuous sequent calculus. The construction of an l-group from a sequent calculus involves simple finitary proof rules using rational numbers. In particular, the group operations are captured by constructing certain entailments capturing informally how 'continuous real functions' are related by their behavior on rational numbers. As an illustration of the techniques, we can show that every archimedean l-group with strong order unit is commutative without recourse to non-constructive real numbers. <br />
<br />
'''[http://mathcs.chapman.edu/~jipsen/seminarposters/Moshier_092211.pdf Poster]'''<br />
<br />
<br />
----<br />
<br />
<br />
=== Thursday, September 15 at 4:00 pm in VN 116 ===<br />
<br />
''Speaker:'' '''Professor Yakir Aharonov, [http://www.chapman.edu Chapman University] and [http://www.chapman.edu/ACFS/Quantum/default.asp Center of Excellence in Quantum Studies]'''<br />
<br />
''Title:'' '''Can the future affect the present without violating causality?'''<br />
<br />
''Abstract:'' I will discuss properties of pre- and post-selected ensembles in quantum mechanics and the way to observe these properties through the use of a new type of non-disturbing measurement called 'weak measurement'. A number of these new experiments have already been successfully performed.<br />
<br />
I will also discuss another type of measurement which does not disturb the observed quantum system. The main result of this new approach is the realization that the basic difference between classical and quantum mechanics is the non-local aspects of quantum dynamics.<br />
<br />
Theoretical analysis of the outcomes of these experiments have produced several very rich results. First, it has shed new light on the most puzzling features of quantum mechanics, such as interference, entanglement, etc. Secondly, it has uncovered a host of new quantum phenomena, which were previously hidden.<br />
<br />
'''[http://mathcs.chapman.edu/~jipsen/seminarposters/Aharonov_090811.pdf Poster]'''<br />
<br />
<br />
----<br />
<br />
<br />
=== Thursday, September 8 at 4:00 pm in VN 116 ===<br />
<br />
''Speaker:'' '''Professor Steven Krantz, [http://wustl.edu/ Washington University in St. Louis]'''<br />
<br />
''Title:'' '''A Matter of Gravity'''<br />
<br />
''Abstract:'' We treat the concept of "center of gravity" from a new point of view. We derive<br />
a number of original results about the stability of the center of gravity.<br />
<br />
We also study asymptotic features of the center of gravity as the dimension of<br />
the ambient space tends to infinity.<br />
<br />
These results are of interest to roboticists and to physicists who study quantum mechanics.<br />
But they also have intrinsic mathematical merit.<br />
<br />
The talk will be accessible to anyone who has had multi-variable calculus.<br />
<br />
'''[http://mathcs.chapman.edu/~jipsen/seminarposters/Krantz_090811.pdf Poster]'''<br />
<br />
<br />
----<br />
<br />
== Spring 2011 ==<br />
<br />
<br />
=== Tuesday, May 24 at 4:00 pm in VN 116 ===<br />
<br />
''Speaker:'' '''Dr. David Carfì, Researcher and Aggregate Professor, Faculty of Economics, University of Messina, Visiting Researcher at University of California Riverside'''<br />
<br />
''Title:'' '''Dirac Calculus in distribution spaces for Quantum Mechanics and Economics'''<br />
<br />
''Abstract:'' In his famous treatise “Principles of Quantum Mechanics” (1930), the great mathematician and physicist Paul Dirac introduced several “manipulation rules” for vectors and operators of linear spaces, which together constitute the so-called “Dirac Calculus”. This Calculus is nothing more than a wide set of formal extensions of the basic properties of the finite-dimensional Linear Algebra to the case of infinite-dimensional vector spaces. The discourse is elegant and surprisingly efficient, but it is far from being a rigorous mathematical treatment. As mathematicians well know, the passage from the finite to the infinite dimensional case does not amount to a mere substitution of finite linear combinations with formal integrals!<br />
<br />
The goal of the research introduced in this talk is to give a precise mathematical meaning and rigorous support to many analytic methods of Quantum Mechanics, starting from the fundamental Dirac Calculus, using the Weak Duality Theory of L. Schwartz and J. A. Dieudonné and the L. Schwartz Theory of Distributions. This approach will give a rigorous justification for the use of Dirac's tools, leaving them substantially “as they are” in Quantum Mechanics practice. Moreover, by providing a correct interpretation of these heuristic methods in terms of new solid and powerful mathematical entities and concepts, we will be helped in reaching a deeper understanding of the physical structures studied in Quantum Mechanics.<br />
<br />
The new operations of continuous-superposition and that of the Dirac product allow us to build - in a mathematically rigorous way - the "extended Linear Algebra" of Dirac in the spaces of tempered distributions, via their natural topological linear structures. More precisely, we shall see that the algebraic-topological structure of tempered distribution spaces allows us to define - naturally - the linear combinations of a continuous family of vectors and operators and a scalar product (of a vector by such continuous families of vectors) which are absolutely necessary (and already formally introduced and used by Dirac himself) for the modern theoretical development of Quantum Mechanics.<br />
<br />
<br />
----<br />
<br />
<br />
=== Monday and Tuesday, April 4 and April 5, at 2:30 pm in VN 116 ===<br />
<br />
''Speaker:'' '''Dr. Henry Stapp (Lawrence Berkeley National Laboratory)'''<br />
<br />
''Title:'' '''Discussions on quantum issues and their mathematical foundations'''<br />
<br />
''Abstract:'' Discussions on quantum issues and their mathematical foundations. <br />
<br />
<br />
----<br />
<br />
<br />
=== Thursday, March 7, at 4:30 pm in VN 116 ===<br />
<br />
''Speaker:'' '''Dr. Neil Donaldson (UCI)'''<br />
<br />
''Title:'' '''Isothermic surfaces - an overview'''<br />
<br />
''Abstract:'' In this talk we consider some of the structure of classical isothermic surfaces; those for which there exist conformal curvature line co-ordinates. We moreover consider two modern approaches/generalizations of the classical theory which place the discussion firmly in the realm of integrable systems.<br />
<br />
<br />
----<br />
<br />
<br />
=== January 10 - January 19, 2011 in VN 116 ===<br />
<br />
<br />
'''THIRD ANNUAL [http://mathcs.chapman.edu/CECAT CECAT] WORKSHOP IN POINTFREE TOPOLOGY & ANALYSIS'''<br />
<br />
(see also the [http://mathcs.chapman.edu/CECAT/workshops.html CECAT workshops] page)<br />
<br />
<TABLE><br />
<TR><br />
<TD><STRONG>Monday 10th:</STRONG></TD><br />
<TD>12pm-2pm</TD><br />
<TD><STRONG>Bernhard Banaschewski (McMaster University, Canada)</STRONG></TD></TR><br />
<TR><br />
<TD></TD><br />
<TD></TD><br />
<TD>"Essential completions - update"</TD></TR><br />
<TR><br />
<TD></TD><br />
<TD>3pm-5pm</TD><br />
<TD><STRONG>Olaf Klinke (University of Birmingham, UK)</STRONG></TD></TR><br />
<br />
<TR><br />
<TD></TD><br />
<TD></TD><br />
<TD>"Pointfree bitopological compactification"</TD></TR><br />
<TR><br />
<TD></TD><br />
<TD></TD><br />
<TD>&nbsp;</TD></TR><br />
<TR><br />
<TD><STRONG>Tuesday 11th:</STRONG></TD><br />
<TD>10am-12pm</TD><br />
<TD><STRONG>Bernhard Banaschewski</STRONG></TD></TR><br />
<TR><br />
<br />
<TD></TD><br />
<TD></TD><br />
<TD>"Essential completions - update"</TD></TR><br />
<TR><br />
<TD></TD><br />
<TD>2pm-4pm</TD><br />
<TD>Open session</TD></TR><br />
<TR><br />
<TD></TD><br />
<TD></TD><br />
<TD>&nbsp;</TD></TR><br />
<TR><br />
<TD><STRONG>Wednesday 12th:</STRONG></TD><br />
<br />
<TD>12pm-2pm</TD><br />
<TD><STRONG>Bernhard Banaschewski</STRONG></TD></TR><br />
<TR><br />
<TD></TD><br />
<TD></TD><br />
<TD>"Essential completions - update"</TD></TR><br />
<TR><br />
<TD></TD><br />
<TD>3pm-5pm</TD><br />
<TD><STRONG>Andrew Moshier (Chapman University)</STRONG></TD></TR><br />
<TR><br />
<TD></TD><br />
<br />
<TD></TD><br />
<TD>"Another Duality for Commutative C* Algebras"</TD></TR><br />
<TR><br />
<TD></TD><br />
<TD></TD><br />
<TD>&nbsp;</TD></TR><br />
<TR><br />
<TD><STRONG>Thursday 13th:</STRONG></TD><br />
<TD></TD><br />
<TD>No scheduled talks</TD></TR><br />
<TR><br />
<TD></TD><br />
<TD></TD><br />
<TD>&nbsp;</TD></TR><br />
<br />
<TR><br />
<TD><STRONG>Friday 14th:</STRONG></TD><br />
<TD>11am-1pm</TD><br />
<TD><STRONG>Bernhard Banaschewski</STRONG></TD></TR><br />
<TR><br />
<TD></TD><br />
<TD></TD><br />
<TD>"Extended real-valued functions"</TD></TR><br />
<TR><br />
<TD></TD><br />
<TD>2pm-4pm</TD><br />
<TD>Open session</TD></TR><br />
<br />
<TR><br />
<TD></TD><br />
<TD>5pm - 7pm</TD><br />
<TD>Drinks and snacks at Von Neumann Hall</TD></TR><br />
<TR><br />
<TD></TD><br />
<TD></TD><br />
<TD>&nbsp;</TD></TR><br />
<TR><br />
<TD><STRONG>Saturday 15th:</STRONG></TD><br />
<TD>10am</TD><br />
<TD>Coffee at Café Lucas</TD></TR><br />
<br />
<TR><br />
<TD></TD><br />
<TD>11am-1pm</TD><br />
<TD><STRONG>Bernhard Banaschewski</STRONG></TD></TR><br />
<TR><br />
<TD></TD><br />
<TD></TD><br />
<TD>"Extended real-valued functions"</TD></TR><br />
<TR><br />
<TD></TD><br />
<TD>2pm-4pm</TD><br />
<TD><STRONG>Andrew Moshier</STRONG></TD></TR><br />
<br />
<TR><br />
<TD></TD><br />
<TD></TD><br />
<TD>"Integration in Logical Form"</TD></TR><br />
<TR><br />
<TD></TD><br />
<TD></TD><br />
<TD>&nbsp;</TD></TR><br />
<TR><br />
<TD><STRONG>Sunday 16th:</STRONG></TD><br />
<TD>10am-12pm</TD><br />
<TD><STRONG>Rick Ball (University of Denver)</STRONG></TD></TR><br />
<TR><br />
<br />
<TD></TD><br />
<TD></TD><br />
<TD>"Integration ideas in a pointfree context"</TD></TR><br />
<TR><br />
<TD></TD><br />
<TD>1pm-3pm</TD><br />
<TD>Open session</TD></TR><br />
<TR><br />
<TD></TD><br />
<TD></TD><br />
<TD>&nbsp;</TD></TR><br />
<TR><br />
<TD><STRONG>Monday 17th:</STRONG></TD><br />
<br />
<TD>12pm-2pm</TD><br />
<TD><STRONG>Bernhard Banaschewski</STRONG></TD></TR><br />
<TR><br />
<TD></TD><br />
<TD></TD><br />
<TD>"Extended real-valued functions"</TD></TR><br />
<TR><br />
<TD></TD><br />
<TD>3pm-5pm</TD><br />
<TD>Open session</TD></TR><br />
<TR><br />
<TD></TD><br />
<br />
<TD></TD><br />
<TD>&nbsp;</TD></TR><br />
<TR><br />
<TD><STRONG>Tuesday 18th:</STRONG></TD><br />
<TD>10am-12pm</TD><br />
<TD><STRONG>Bernhard Banaschewski</STRONG></TD></TR><br />
<TR><br />
<TD></TD><br />
<TD></TD><br />
<TD>"To be announced"</TD></TR><br />
<TR><br />
<TD></TD><br />
<TD>2pm-4pm</TD><br />
<br />
<TD>Open session</TD></TR><br />
<TR><br />
<TD></TD><br />
<TD></TD><br />
<TD>&nbsp;</TD></TR><br />
<TR><br />
<TD><STRONG>Wednesday 19th:</STRONG></TD><br />
<TD>12pm-2pm</TD><br />
<TD><STRONG>Bernhard Banaschewski</STRONG></TD></TR><br />
<TR><br />
<TD></TD><br />
<TD></TD><br />
<TD>"To be announced"</TD></TR><br />
<br />
<TR><br />
<TD></TD><br />
<TD>3pm-5pm</TD><br />
<TD>Open session</TD></TR></TABLE></div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=MathCS_Seminar_2012&diff=12MathCS Seminar 20122021-02-22T18:34:34Z<p>Jipsen: Created page with "''Seminar Organizers:'' Peter Jipsen and Cyril Rakovski == Fall 2012 == === Thursday, November 15, 2012 at 2 pm - 5 pm in VN === ==== Third [http://www.chapman.edu Chapman..."</p>
<hr />
<div>''Seminar Organizers:'' Peter Jipsen and Cyril Rakovski<br />
<br />
== Fall 2012 ==<br />
<br />
=== Thursday, November 15, 2012 at 2 pm - 5 pm in VN ===<br />
<br />
==== Third [http://www.chapman.edu Chapman University] and [http://www.fullerton.edu Cal State University Fullerton] Joint Mathematics Colloquium ====<br />
<br />
held at '''Chapman University, Von Neumann Hall''' (545 W. Palm Ave, Orange)<br />
meet at 1:30 pm in Von Neumann Hall for a brief reception<br />
<br />
'''PROGRAM'''<br />
<br />
'''2:00 pm Lucy Odom (CSU Fullerton)''' - "Amalgamatic Curvature and Absolute Umbilical Hypersurfaces"<br />
<br />
'''2:25 pm David Tyler (Chapman University)''' - "Map the Network"<br />
<br />
'''2:50 pm Charley Conley (CSU Fullerton)''' - "A Rigidity Theorem for Hypersurfaces"<br />
<br />
'''3:15 pm Adrian Vajiac (Chapman University)''' - "Bicomplex Numbers"<br />
<br />
'''3:40 pm Coffee Break<br />
<br />
'''4:10 pm Nicholas Salinas (CSU Fullerton)''' - "Polynomial Isometries of P-adic Integers"<br />
<br />
'''4:35 pm Peter Jipsen (Chapman University)''' - "A Category of Algebraic Contexts equivalent to Idempotent Semirings"<br />
<br />
<br />
----<br />
<br />
<br />
=== Monday, October 22 -- Friday, October 26 2012 ===<br />
<br />
==== Workshop on Function Theories for Bicomplex and Hyperbolic Numbers ====<br />
<br />
Hosted by the '''Center of Excellence in Complex and Hypercomplex Analysis (CECHA)'''<br />
<br />
'''PROGRAM'''<br />
<br />
'''Monday October 22nd 2012'''<br />
<br />
9:30am-10:30am '''Adrian Vajiac, Chapman University'''<br />
<br />
Title: “Bicomplex Analysis: an introduction”<br />
<br />
10:45am-11:45am '''Michael Shapiro, Instituto Politecnico Nacional, Mexico'''<br />
<br />
Title: “Bicomplex Derivability, Differentiability, and Holomorphy”<br />
<br />
2:00pm-3:00pm '''John Ryan, University of Arkansas'''<br />
<br />
Title: “Complex Clifford Analysis”<br />
<br />
3:15pm-4:15pm '''Craig Nolder, Florida State University'''<br />
<br />
Title: “Conformal Mappings in R1,1 are Quasi-Conformal”<br />
<br />
----<br />
<br />
'''Tuesday October 23rd 2012'''<br />
<br />
9:30am-10:30am '''Elena Luna Elizarraras, Instituto Politecnico Nacional, Mexico'''<br />
<br />
Title: “On Fundamentals of Functional Analysis with Bicomplex Scalars”<br />
<br />
10:45am-11:45am '''Dominic Rochon, Université du Québec à Trois-Rivières, Canada'''<br />
<br />
Title: “Infinite Dimensional Bicomplex Hilbert Spaces“<br />
<br />
2:00pm-3:00pm '''Daniele Struppa, Chapman University'''<br />
<br />
Title: “Holomorphic functions of a bicomplex variable and Ehrenpreis’ Fundamental Principle”<br />
<br />
3:15pm-4:15pm '''Franciscus Sommen, Universiteit Gent, Belgium'''<br />
<br />
Title: “Spherical Monogenics on the Lie Sphere” <br />
<br />
----<br />
<br />
'''Wednesday October 24th 2012'''<br />
<br />
9:30am-10:30am '''Uwe Kahler, University of Aveiro, Portugal'''<br />
<br />
Title: “Discrete Function theories in the case of bicomplex and hyperbolic numbers“<br />
<br />
10:45am-11:45am '''Paula Cerejeiras, University of Aveiro, Portugal'''<br />
<br />
Title: “On the Gabor Transform: the Bicomplex Case”<br />
<br />
----<br />
<br />
'''Thursday October 25th 2012'''<br />
<br />
9:30am-10:30am '''Daniel Alpay, Ben-Gurion University of the Negev, Israel'''<br />
<br />
Title: “Schur Analysis and Theory of Linear Systems: The Bicomplex Case“<br />
<br />
10:45am-11:45am '''Sebastien Tremblay, Université du Québec à Trois-Rivières, Canada'''<br />
<br />
Title: “Hyperbolic Pseudonanalytic Functions in Mathematical Physics“<br />
<br />
2:00pm-3:00pm '''Irene Sabadini, Politecnico di Milano, Italy'''<br />
<br />
Title: “Algebraic Analysis Methods in the Bicomplex setting “<br />
<br />
3:15pm-4:15pm '''Fabrizio Colombo, Politecnico di Milano, Italy'''<br />
<br />
Title: “Bicomplex Holomorphic Functional Calculus “<br />
<br />
----<br />
<br />
'''Friday October 26th 2012'''<br />
<br />
9:30am-10:30am '''Matvei Libine, Indiana University'''<br />
<br />
Title: “Introduction to Split Quaternionic Analysis “<br />
<br />
10:45am-11:35am '''Mihaela Vajiac, Chapman University'''<br />
<br />
Title: “Hyperbolic Analysis: an introduction”<br />
<br />
<br />
----<br />
<br />
<br />
=== Thursday, October 4, 2012 at 1:15 pm in VN 116 ===<br />
<br />
''Speaker:'' '''[http://www.chapman.edu/our-faculty/m-andrew-moshier Prof. Andrew Moshier], Faculty of Computer Science and Mathematics, [http://www.chapman.edu Chapman University]'''<br />
<br />
''Title:'' '''Generalizing Modal Logic for Compact Hausdorff Semantics'''<br />
<br />
''Abstract:'' Normal modal logic can be regarded as a specification language for non-deterministic<br />
state transition systems, modeled as compact, zero-dimensional topological spaces equipped<br />
with a closed binary relation. The zero-dimensionality requirement, however, severely limits<br />
potential applications. After all, this rules out such state spaces as spheres, tori and other<br />
garden variety compact Hausdorff spaces.<br />
<br />
In this talk we consider how to generalize descriptive frames to allow for compact Hausdorff<br />
state spaces, and then ask how modal logic can be adapted to this generalization. In<br />
the result, we show that a Sahlqvist Theorem holds, characterizing a class of formulas that<br />
determine first-order definable properties of the state transition.<br />
<br />
This is joint work with [http://www.doc.ic.ac.uk/~nbezhani/ Nick Bezhanishvili].<br />
<br />
<br />
----<br />
<br />
<br />
=== Tuesday, August 28, 2012 at 4 pm in VN 116 ===<br />
<br />
''Speaker:'' '''[http://web.cs.du.edu/~petr/ Dr. Petr Vojtechovsky], [http://www.du.edu/nsm/departments/mathematics/ Department of Mathematics], [http://www.du.edu University of Denver]'''<br />
<br />
''Title:'' '''Computational aspects of loop theory'''<br />
<br />
''Abstract:'' Loop theory is closely related to group theory, but the lack of associativity makes calculations with loops difficult. Since 2000, there has been notable progress in several areas of loop theory thanks to a variety of computational tools, including group-theoretical packages, symbolic computation systems, automated theorem provers and finite model builders. In this talk I will present four projects where these computational tools were essential, although one would probably not have guessed it from the results alone. I will not assume any prior knowledge of loop theory in the talk.<br />
<br />
<br />
----<br />
<br />
<br />
== Spring 2012 ==<br />
<br />
<br />
=== Thursday, May 10, 2012 at 4 pm in VN 116 ===<br />
<br />
''Speaker:'' '''[http://www.cs.le.ac.uk/people/akurz/ Dr. Alexander Kurz], [http://www.le.ac.uk/ University of Leicester], UK'''<br />
<br />
''Title:'' '''Categories definable by operations and equations'''<br />
<br />
''Abstract:'' It is widely accepted that the category theoretic notion of a monad captures abstractly the idea of an algebraic theory. Indeed, a theorem of Linton 1969 says that the algebras for any monad can be represented by operations and equations if we are willing to generalise the notion of arity. In the talk, we are going to recall the notion of monad and the essence of Linton's argument before giving an application to coalgebras and modal logic (which is joint work with J. Rosicky).<br />
<br />
<br />
----<br />
<br />
=== Friday, April 20, 2012, 2 pm CSU Fullerton ===<br />
<br />
'''Second [http://www.chapman.edu Chapman University] and [http://www.fullerton.edu Cal State University Fullerton] joint Mathematics Colloquium''' held at '''CSU Fullerton, McCarthy Hall 476'''<br />
meet at 1:30 pm in McCarthy Hall 484 for a brief reception<br />
<br />
'''PROGRAM'''<br />
<br />
'''2:00 pm John Simanyi (CSUF undergraduate student) - Complex Series at the Radius of Convergence'''<br />
<br />
''Abstract:'' In complex analysis, as in the real case, we can find a radius of convergence for a given series, dividing the complex plane into separate regions of certain convergence and divergence. What happens at the border, on the circle of precisely that radius? We consider a few examples to investigate.<br />
<br />
<br />
'''2:30 pm Dr. Mark Filowitz (Associate Dean) - Welcoming Address'''<br />
<br />
<br />
'''2:35 pm Alex Barrett (Chapman University, undergraduate student) - A Two-Light Version of the Classical Hundred Prisoners and a Light Bulb Problem: Optimizing Experimental Design through Simulations'''<br />
<br />
''Abstract:'' We propose five original strategies of successively increasing complexity and efficiency that address a novel version of a classical mathematical problem that, in essence, focuses on the determination of an optimal protocol for exchanging limited amounts of information among a group of subjects with various prerogatives. The inherent intricacy of the problem–solving protocols eliminates the possibility to attain an analytical solution. Therefore, we implemented a large-scale simulation study to exhaustively search through an extensive list of competing algorithms associated with the above-mentioned 5 generally defined protocols. Our results show that the consecutive improvements in the average amount of time necessary for the strategy-specific problem-solving completion over the previous simpler and less advantageously structured designs were 18, 30, 12, and 9% respectively. The optimal multi-stage information exchange strategy allows for a successful execution of the task of interest in 1722 days (4.7 years) on average with standard deviation of 385 days. The execution of this protocol took as few as 1004 and as many as 4965 with median of 1616 days.<br />
<br />
<br />
'''3:00 pm Heng Sok (Chapman University, undergraduate student) - On the Performance of Exact Testing Procedures with Respect to Comparisons of Several Multinomial Distributions in Small Samples'''<br />
<br />
''Abstract:'' This research project focuses on the validity of the exact p-value method under the fully specified and non-specified null hypotheses with respect to comparison of multiple multinomial distributions in small samples, where classical chi-square testing procedure is inappropriate. Here by validity, we mean the type I error rates at several significance levels and the power of the test under various alternatives. The two sample comparison problem arises often in two treatment randomized trials and case-control studies where comparison of background characteristics is an important step of the study analysis. Small samples are an inherent trait of pilot studies and studies with recruitment difficulties due to rare conditions, lack of interest and consent or budget and time restrictions. Further, this analysis could be extended to encompass the comparison of more than two multinomial distributions that would be applicable to multiple treatment randomized trials and as done in the classical large sample theory. Our results show that under the non-specified null hypothesis, the exact p-value method is severely conservative due to the absence of adjustment structure in these tests due the estimation of the common parameters and predictably, as the number of sample increases, the type 1 error rate increases but still remains below its nominal level. Consequently, the power of the test is low when the underlying multinomial probability distributions are relatively close to each other and the number of categories is large compared to the sample size.<br />
<br />
<br />
'''3:30 pm Nicholas Blackford, Daniel Lenders, and Danny Orton - An Inverse-Based Analogue of the Probability that Two Elements of a Finite Group Commute'''<br />
<br />
''Abstract:'' Given a finite group G, the probability that two randomly chosen elements of G commute has long been viewed in the literature as a natural measure of the degree of commutativity enjoyed by the group. Many variants on this probabilistic question have arisen in the literature recently, and our research introduces yet another such variation that provides somewhat different information. In particular, given a product of elements of G, we investigate the likelihood of being able to permute the order of the elements in the product and obtain the inverse of the original element. With the help of the software program Groups, Algorithms and Programming (GAP) , we have discovered patterns leading to interesting results about this variant. In our paper, we will examine these patterns for such familiar finite groups as cyclic, dihedral, and symmetric groups, and describe the general results we have obtained. Some of these results are at odds with analogous ones known for the commutativity measure studied in recent articles, thereby adding further interest into our investigation.<br />
<br />
<br />
----<br />
<br />
<br />
=== Friday, April 20, 2012, 1:30 pm in VN 116 ===<br />
<br />
''Speaker:'' '''Dr. Lucas Layton''', <br />
<br />
''Title:'' '''Where the rubber meets the road: How software engineering research can benefit computational science'''<br />
<br />
''Abstract:'' Computational science and software engineering are rarely spoken in the same breath. Heavyweight software development processes are not suited to the dynamic nature of scientific exploration. In this talk, I will present how research on modern software engineering tools, developer practices, and software measurement can be applied to the computational sciences to increase productivity and enable lightweight management of development efforts. I will also discuss the unique research opportunities the Chapman environment can provide to students in software engineering, and how Chapman provides a unique setting studying the important yet neglected intersection of computational science and software engineering.<br />
<br />
<br />
----<br />
<br />
<br />
=== Tuesday, April 17, 2012 at 4pm in VN 116 ===<br />
<br />
''Speaker:'' '''Dr. Erik Linstead, School of Computational Sciences, Schmid College of Science, Chapman University'''<br />
<br />
''Title:'' '''Latent Topic Models for Automated Program Comprehension'''<br />
<br />
''Abstract:'' Software development is a complex and multi-faceted process. In recent years, the open-source movement has made available for the first time an abundance of dynamic software trajectories via the public archiving of software releases. This has fueled new directions of research aimed at visualizing and better understanding software and the people who create it. <br />
<br />
Automated topic modeling has been successfully used in text mining and<br />
information retrieval where it has been applied to the problem of summarizing large text corpora. Recent techniques include Latent Dirichlet Allocation (LDA), which probabilistically models text documents as mixtures of latent topics, where topics correspond to key concepts presented in the corpus. These more recent approaches have been found to produce better results than traditional methods such as latent semantic analysis. Yet despite the capabilities of statistical topic models, applications have typically been limited to traditional text corpora such as academic publications, news reports, and historical documents. At the most basic level, however, a code repository can be viewed as a text corpus, where source files are analogous to documents and tokens to words. Though vocabulary, syntax, and conventions differentiate a programming language from a natural language, the tokens present in a source file are still indicative of its concerns (ie. its topics).<br />
<br />
In this talk we adapt and apply latent topic models to automated program understanding, bug triage, software evolution, and static analysis of software complexity. In particular we provide, for the first time, a formal definition of software scattering and tangling on which to base new software quality metrics. The result of this work is an unsupervised, probabilistic, machine learning framework capable of supporting software analysis on an Internet-scale. Empirical results are presented for several well-known and widely studied open-source software projects, and future research directions in the area of search-driven software development are discussed.<br />
<br />
<br />
----<br />
<br />
<br />
=== Thursday, April 12, 2012 at 4pm in VN 116 ===<br />
<br />
''Speaker:'' '''Professor Greg Fasshauer''', '''Department of Applied Mathematics, [http://www.iit.edu/ Illinois Institute of Technology], Chicago, IL'''<br />
<br />
''Title:'' '''Computing with Positive Definite Kernels'''<br />
<br />
''Abstract:'' <br />
Positive definite kernels and their associated reproducing kernel Hilbert spaces<br />
provide a very flexible and powerful tool for the solution of many typical problems of<br />
numerical analysis and scientific computing such as function approximation, numerical<br />
integration or the numerical solution of PDEs. I will provide an introduction to positive<br />
definite reproducing kernels, mention some applications, and end with a discussion of<br />
some future research directions. This talk should be accessible to upper-level <br />
undergraduate students and beginning graduate students.<br />
<br />
<br />
----<br />
<br />
<br />
=== Tuesday, April 10, 2012 at 4pm in VN 116 ===<br />
<br />
''Speaker:'' '''Dr. Boyana Norris, [http://www.mcs.anl.gov/index.php Mathematics and Computer Science Division], [http://www.anl.gov/ Argonne National Laboratory], Chicago, IL'''<br />
<br />
''Title:'' '''Automatic Differentiation in Computational Science'''<br />
<br />
''Abstract:''<br />
Derivatives play an important role in a wide variety of scientific computing applications, including numerical optimization, solution of nonlinear equations, sensitivity analysis, and nonlinear inverse problems. Automatic differentiation (AD) enables the accurate computation of derivatives via semantic transformation of source code via the application of the rules of differential calculus. By using AD, accurate derivatives can be obtained at a small multiple of the cost of computing the original function, which makes AD more efficient than manual parameter perturbation and finite-difference-based calibration. AD has been widely used in applications in the physical, chemical, biological, and social sciences. <br />
<br />
In this talk, I will introduce AD and describe our approach to enabling efficient automatic differentiation of computational science applications. Our source-transformation AD tools are implemented by using a component-based software engineering approach, enabling reuse of complex capabilities, such as program analysis and the differentiation transformations, while providing separate parsing and code generation components for C, C++, and Fortran. The differentiation process consists of the following steps implemented as loosely coupled components: parsing of the arbitrarily large application source code; performing a number of program analyses; creating a standard, XML-based language-independent intermediate representation of the computational graph; augmenting the computational graph with derivative computations; converting the resulting graph back into the source language's intermediate representation; and finally, producing source code for computing the original function and its derivatives. In addition to existing capabilities, I will discuss a number of open research issues, ranging from mathematical considerations to software engineering challenges in enabling robust and efficient AD in an environment of ever-increasing software and hardware complexity.<br />
<br />
<br />
----<br />
<br />
<br />
=== Thursday, March 22, 2012 at 4pm in VN 116 ===<br />
<br />
''Speaker:'' '''Dr. Mihaela Vajiac, Faculty of Mathematics, [http://www.chapman.edu Chapman University]'''<br />
<br />
''Title:'' '''Examples of Functional Calculus'''<br />
<br />
''Abstract:'' In this talk, I will present examples of Functional Calculus, a subject introduced recently by F. Colombo, I. Sabadini, and D. Struppa, for commuting and non-commuting operators, using different classes of functions. The theory is quite new and lacks examples, a gap which this work is attempting to fill.<br />
<br />
<br />
----<br />
<br />
<br />
=== Tuesday, March 20, 2012 at 4pm in VN 116 ===<br />
<br />
''Speaker:'' '''Eddy Sfeir, [http://www.db.com/usa/ Deutsche Bank], and [http://www.chapman.edu Chapman University] Alumnus'''<br />
<br />
''Title:'' '''Trading Foreign Exchange Options'''<br />
<br />
''Abstract:'' Out of all markets, the currency market is the biggest out there with over 3 Trillion USD exchanging hands every day. From the basic Black-Scholes formula to slightly more advanced concepts such as delta and gamma hedging, the purpose of this talk is to show you what a day in the life of a currency options trader consists of.<br />
<br />
Eddy Sfeir has been trading options for Deutsche Bank for nearly 4 years. He started out on Wall St, and is now trading in London. Deutsche Bank has been number 1 in FX for 7 years in a row (in terms of market share, customer surveys etc.)<br />
<br />
<br />
----<br />
<br />
<br />
=== Thursday, March 15, 2012 at 4pm in VN 116 ===<br />
<br />
''Speaker:'' '''Professor Atanas Radenski, School of Computational Sciences, Schmid College of Science, [http://www.chapman.edu Chapman University]''' <br />
<br />
''Title:'' '''Distributed Simulated Annealing with MapReduce on the Cloud'''<br />
<br />
''Abstract:'' Simulated annealing’s high computational intensity has stimulated researchers to experiment with various annealing algorithms for shared memory, message-passing, and hybrid-parallel platforms. MapReduce is an emerging distributed computing framework for large-scale data processing on clusters of commodity servers; to our knowledge, MapReduce has not been used for simulated annealing yet. In this talk, we investigate the applicability of MapReduce to distributed simulated annealing in general, and to the TSP in particular. We (i) outline six algorithmic patterns of distributed simulated annealing with MapReduce, (ii) discuss the instantiation of such patterns into MR implementations to solve sample TSP problems, and (iii) evaluate solution quality and speedup of the implementations on a cloud computing platform, Amazon’s Elastic MapReduce. The talk can be beneficial for those interested in the potential of cloud-based MapReduce in computationally intensive methods in general and nature-inspired algorithms in particular.<br />
<br />
'''[http://mathcs.chapman.edu/~jipsen/seminarposters/Radenski_20120315.pdf Poster]'''<br />
<br />
<br />
----<br />
<br />
<br />
=== Thursday, February 23, 2012 at 12 noon in VN 116 ===<br />
<br />
<br />
''Speaker:'' '''Dr. Roman Buniy, Faculty of Physics, [http://www.chapman.edu Chapman University]''' <br />
<br />
''Title:'' '''New measures for entangled states'''<br />
<br />
''Abstract:'' We propose new measures that distinguish and classify entangled states. The measures are algebraic invariants of linear maps associated with the states. Considering qubits as well as higher spin systems, we obtained complete entanglement classifications for cases that were either unsolved or only conjectured in the literature.<br />
<br />
'''[http://mathcs.chapman.edu/~jipsen/seminarposters/Buniy_20120223.pdf Poster]'''<br />
<br />
<br />
----<br />
<br />
<br />
=== Wednesday, February 1, 2012 at 4:00 pm in VN 116 ===<br />
<br />
<br />
''Speaker:'' '''Professor Aleš Pultr, [http://www.cuni.cz/UKENG-1.html Charles University], Prague, Czech Republic'''<br />
<br />
''Title:'' '''Algebraic and Topological Aspects of the Coproduct of Frames'''<br />
<br />
''Abstract:'' The algebraic aspects concern the coproduct as the tensor product in a broader category.<br />
This is the same phenomenon as the coproduct of commutative rings being<br />
carried by the tensor product of the underlying abelian groups, and we will<br />
consider how it is in a general setting.<br />
<br />
The topological aspects are related to confronting the coproduct $\Omega(X)\otimes\Omega(Y)$ with<br />
the product $X\times Y$.<br />
<br />
The consequences of the discrepancy are generally pleasant, as can be seen in the behaviour of paracompact<br />
frames, the closed subgroup theorem, and a pleasant situation in confronting cover and entourage uniformity.<br />
<br />
<br />
----<br />
<br />
<br />
=== January 9 - January 19, 2012 in VN 116 ===<br />
<br />
<br />
'''FOURTH ANNUAL CECAT WORKSHOP IN POINTFREE TOPOLOGY & ANALYSIS'''<br />
<br />
<table><br />
<tr><td>'''Monday 9th:'''<td>12pm-2pm<td>'''Bernhard Banaschewski (McMaster University, Canada)'''<br />
<tr><td><td><td>"Pseudocompactness in Frames"<br />
<br />
<tr><td><td>2.30pm-3.30pm<td>'''Drew Moshier (Chapman University)'''<br />
<tr><td><td><td>"D-frames"<br />
<br />
<tr><td>'''Tuesday 10th:'''<td>10am-12pm<td>'''Drew Moshier'''<br />
<tr><td><td><td>"D-frames"<br />
<br />
<tr><td><td>12.30pm-2.30pm<td>'''Bernhard Banaschewski'''<br />
<tr><td><td><td>"Pseudocompactness in Frames"<br />
<br />
<tr><td>'''Wednesday 11th:'''<td><td>No scheduled talks<br />
<br />
<tr><td>'''Thursday 12th:'''<td>11am-1pm<td>'''Drew Moshier'''<br />
<tr><td><td><td>"D-frames"<br />
<br />
<tr><td><td>1.30pm-3.30pm<td>'''Bernhard Banaschewski'''<br />
<br />
<tr><td>'''Friday 13th:'''<td>10.30am-noon<td>'''Bernhard Banaschewski'''<br />
<tr><td><td><td>"The rings of continuous functions on sigma frames"<br />
<br />
<tr><td><td>12.30pm-2pm<td>'''Drew Moshier'''<br />
<tr><td><td><td>"A relational category of formal contexts"<br />
<br />
<tr><td>'''Saturday 14th:'''<td>10.30am-noon<td>'''Bernhard Banaschewski'''<br />
<tr><td><td><td>"The rings of continuous functions on sigma frames"<br />
<br />
<tr><td><td>12.30-2pm<td>'''Rick Ball (University of Denver, joint work with Tony Hager)'''<br />
<tr><td><td><td>"Truncated and diminished l-groups"<br />
<br />
<tr><td><td>2.30pm-4pm<td>'''Garth Dales (University of Lancaster, UK)'''<br />
<tr><td><td><td>"The hyper-Stonean cover of a compact space"<br />
<br />
<tr><td>'''Sunday 15th:'''<td>10.30am-noon<td>'''Bernhard Banaschewski'''<br />
<tr><td><td><td>"The rings of continuous functions on sigma frames"<br />
<br />
<tr><td><td>12.30-2pm<td>'''Rick Ball (joint work with Tony Hager)'''<br />
<tr><td><td><td>"Truncated and diminished l-groups"<br />
<br />
<tr><td><td>4pm<td>'''Cello Concert followed by informal reception'''<br />
<br />
<tr><td>'''Monday 16th:'''<td>10am<td>Coffee at Café Lucas<td><br />
<tr><td><td>11am-1pm<td>'''Rick Ball (joint work with Tony Hager)'''<br />
<tr><td><td><td>"Truncated and diminished l-groups"<br />
<br />
<tr><td><td>1.30pm-3pm<td>'''Peter Jipsen (Chapman University)'''<br />
<tr><td><td><td>"On the duality between lattices and topological contexts"<br />
<br />
<tr><td>'''Tuesday 17th:'''<td>10am-12pm<td>'''Bernhard Banaschewski'''<br />
<tr><td><td><td>"TBD"<br />
<br />
<tr><td><td>12:30pm-2pm<td>'''Peter Jipsen'''<br />
<tr><td><td><td>"On the duality between lattices and topological contexts"<br />
<br />
<tr><td>'''Wednesday 18th:'''<td><td>No scheduled talks<br />
<br />
<tr><td>'''Thursday 19th:'''<td>11am-2.30pm<td>'''Open session'''<br />
<tr><td><td><td>"D-frames"<br />
</table><br />
<br />
<br />
----</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=MathCS_Seminar_2013&diff=11MathCS Seminar 20132021-02-22T18:33:59Z<p>Jipsen: Created page with " == Fall 2013 == === Thursday, Nov 21, 2013 from 2 pm to 4 pm in VN 116 === ==== Fifth [http://www.fullerton.edu Cal State University Fullerton] and [http://www.chapman.edu..."</p>
<hr />
<div><br />
== Fall 2013 ==<br />
<br />
=== Thursday, Nov 21, 2013 from 2 pm to 4 pm in VN 116 ===<br />
<br />
==== Fifth [http://www.fullerton.edu Cal State University Fullerton] and [http://www.chapman.edu Chapman University] Joint Mathematics Colloquium ====<br />
<br />
''Organizers:'' '''Bogdan Suceavă''' (CSUF) and '''Peter Jipsen''' (Chapman University)<br />
<br />
''Program'' <br />
<br />
2:00 - 2:20 '''Fernando Quintino''' (Cal State Fullerton)<br><br />
'''Interpolating Legendre Multiplier Sequences'''<br />
<br />
2:20 - 2:40 '''Allie Smith and Louis Ehwerhemuepha''' (Chapman University)<br> <br />
'''A Novel Exact Test for Association for Small Sample Case-Control Studies<br />
<br />
2:40 - 3:00 '''Nathan Robertson, Susan Deeb, Soeun Park, and Reina Galvez''' (Cal State Fullerton)<br> <br />
'''A Comparative Analysis of Three Clustering Techniques with an Application to K6-11 Mathematics Achievement Data'''<br />
<br />
3:00 - 3:20 '''Kevin Gomez''' (Cal State Fullerton)<br><br />
'''A Ladder of Curvatures for Hypersurfaces in the Euclidean Ambient Space'''<br />
<br />
3:20 - 3:40 '''Melissa Riddle''' (Cal State Fullerton)<br><br />
'''A Pinching Theorem for Three-Dimensional Hypersurfaces in Euclidean Ambient Space'''<br />
<br />
3:40 - 4:00 '''Kyle Lee''' (Chapman University)<br><br />
'''Investigating Quantum Gravity through Causal Dynamical Triangulations'''<br />
<br />
<br />
[http://mathcs.chapman.edu/~jipsen/seminarposters/Joint_Colloquium_Chapman_CSUF5.pdf PDF file with abstracts]<br />
<br />
<br />
<!--'''Other seminar talks and events (subject to change):'''--><br />
<br />
<br />
----<br />
<br />
<br />
=== Wednesday, Nov 13, 2013 at 12 noon in VN 116 ===<br />
<br />
==== ''Speaker:'' '''Professor Daniele Struppa, Chapman University''' ====<br />
<br />
''Title:'' '''Propagation of superoscillations as solutions to the Cauchy problem for generalized Schrodinger equations'''<br />
<br />
''Abstract:'' Superoscillatory sequences have been introduced by Yakir Aharonov (and discussed in a series of seminars last year) as a byproduct of his theory of weak measurement. In this talk I will show that if we consider the Schrodinger equation (and some natural generalizations of it) , with superoscillatory initial conditions, the solution of the equation maintains superoscillatory behavior. The fundamental instruments necessary to prove such a result are the Fourier transform, and some results in the theory of convolution operators on spaces of rapidly growing entire functions (Berenstein and Struppa, Publ. RIMS Kyoto, 1988). The results that I will describe are the subject of three recent papers (coauthored with Aharonov, Colombo, Sabadini, and Tollaksen), the first of which has appeared in Journ. Math. Pures et Appliques, 2013.<br />
<br />
<br />
----<br />
<br />
<br />
=== Wednesday, Oct 23, 2013 at 12 noon in VN 116 ===<br />
<br />
==== ''Speaker:'' '''Professor Atanas Radenski''', '''Chapman University''' ====<br />
<br />
''Title:'' '''MapReduce Streaming Algorithms for Laplace Relaxation on the Cloud'''<br />
<br />
''Abstract:'' I will begin this presentation with a gentle introduction to MapReduce parallelism. No preliminary knowledge of MapReduce is expected (but this presentation will be an opportunity to gain some MapReduce understanding). Technically, I will describe relaxation algorithms for the Laplace equation in MR streaming, and evaluate empirically their performance on Elastic MR, the Amazon MR cloud. These results can be beneficial to others who would like to develop and optimize MR streaming algorithms for grid-based models, such as PDE and cellular automata.<br />
<br />
<br />
----<br />
<br />
<br />
=== Wednesday, Sept 18, 2013 at 12 noon in VN 116 ===<br />
<br />
==== ''Speaker:'' '''Dr. Tadeusz Litak''', '''Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany''' ====<br />
<br />
''Title:'' '''Friends, Likes and Coalitions: Coalgebraic Predicate Logic in Action'''<br />
<br />
''Abstract:'' The talk is about a joint work with Dirk Pattinson, Katsuhiko Sano and Lutz Schröder.<br />
It is about a generalization of first-order logic: a natural and generic language for non-relational structures which can be recast as Set-coalgebras.<br />
However, I will assume no familiarity with coalgebras and coalgebraic logic. It is enough to know that the framework<br />
can cover such diverse structures as Kripke frames, neighbourhood frames, topological spaces, discrete Markov chains,<br />
conditional frames, multigraphs or game frames for coaliton logic/alternating time logics. As a taster, we will develop<br />
an apparatus to reason about activities and preferences in social networks. Then we will shortly discuss issues likes<br />
completeness, model theory and proof theory.<br />
<br />
<br />
----<br />
<br />
== Spring 2013 ==<br />
<br />
<br />
=== Friday, April 26, 2013 at 2 pm - 5 pm Cal State Fullerton ===<br />
<br />
==== Fourth [http://www.fullerton.edu Cal State University Fullerton] and [http://www.chapman.edu Chapman University] Joint Mathematics Colloquium ====<br />
<br />
<br />
''Program'' <br />
<br />
'''Casey Coleman and Adrian Vajiac''' (Chapman University)<br />
<br />
''Title:'' '''A New Perspective on Geometry: Polynomials and Curved Spaces''' (Research Adviser: Dr. Adrian Vajiac)<br />
<br />
'''Robert Giza''' (Cal Poly Pomona)<br />
<br />
''Title:'' '''Series associated with multifractal analysis''' (Research adviser: Dr. John Rock)<br />
<br />
'''Duy D Ngo, Reina R Galvez, and Antouneo Kassab''' (Cal State Fullerton)<br />
<br />
''Title:'' '''A Multivariate Statistical Inference for the Analysis of Neuronal Spiking Rates''' (Research adviser: Dr. Sam Behseta)<br />
<br />
'''Nathan Lawless''' (Chapman University)<br />
<br />
''Title:'' '''Generating all modular lattices of a given size''' (Research adviser: Dr. Peter Jipsen)<br />
<br />
'''Yusuf Jabri''' (Cal Poly Pomona)<br />
<br />
''Title:'' '''Genesis of the ubiquitous Fibonacci Word''' <br />
<br />
'''Jenny Chang''' (Cal State Fullerton)<br />
<br />
''Title:'' '''Robust Statistical Modeling of Neuronal Intensity Rates''' (Research adviser: Dr. Sam Behseta)<br />
<br />
'''Cody Gruebele''' (Cal State Fullerton)<br />
<br />
''Title:'' '''Comparison of Two Models For Fat/Water Separation in Magnetic Resonance Imaging (MRI)''' (Research adviser: Dr. Angel Pineda)<br />
<br />
<br />
[http://mathcs.chapman.edu/~jipsen/seminarposters/Joint_Colloquium_Chapman_CSUF.pdf PDF file with abstracts]<br />
<br />
<br />
<br />
----<br />
<br />
=== Wednesday, April 24, 2013 at 2:30 pm in VN 116 ===<br />
<br />
==== ''Speaker:'' '''Cynthia Northrup''', '''University of California, Irvine''' ====<br />
<br />
''Title:'' '''Using Forcing to Obtain a Model of the Continuum Hypothesis'''<br />
<br />
''Abstract:'' Forcing is a method used to extend a transitive model M by adjoining a new set G in<br />
order to obtain a larger transitive model M[G]. Our choice of partial order, or notion of<br />
forcing, determines what is true in M[G]. We will consider the forcing introduced by Paul<br />
Cohen in proving the independence of the Continuum Hypothesis. The Diamond Principle,<br />
introduced by Jensen in 1972, can be thought of as a strengthening of the Continuum<br />
Hypothesis. From a diamond sequence of length k we can read off all of the subsets of k.<br />
We are interested in using an iteration involving Radin forcing in order to obtain a model<br />
of the failure of Diamond.<br />
<br />
<br />
----<br />
<br />
<br />
=== Tuesday, April 23, 2013 at 1:15 pm in VN 116 ===<br />
<br />
==== ''Speaker:'' '''Dr. Papiya Bhattacharjee''', '''Penn State Erie, The Behrend College''' ====<br />
<br />
''Title:'' '''Extensions in Algebraic Frames'''<br />
<br />
''Abstract:'' A frame L is algebraic if every element of L is expressed as a supremum of compact elements. In case of algebraic frames L that also satisfy the Finite Intersection Property, we investigate the spaces of minimal prime elements of L, called Min(L), with respect to the Zariski topology and the Inverse topology. The first part of the talk will describe these spaces. Finally, given two algebraic frames L and M (L is a subframe of M), the speaker will describe various extensions such as Rigid extension, r-extension, etc. and their relationship with the spaces of Min(L). In particular, it turns out that if M is a rigid frame extension of L, then Min(L) is homeomorphic to Min(M) with respect to both the Zariski topology and the inverse topology.<br />
<br />
<br />
----<br />
<br />
<br />
=== Wednesday, April 17, 2013 at 2:30 pm in VN 116 ===<br />
<br />
==== ''Speaker:'' '''Andres Forero Cuervo''', '''University of California, Irvine''' ====<br />
<br />
''Title:'' '''Sets With No Length, Alternative Axioms and Infinite Games'''<br />
<br />
''Abstract:'' The length of a subset of the real line can be defined in mathematical terms. A set of real numbers is called "measurable" if a precise, definite length can be assigned to it, following certain desired natural properties. Surprisingly, from the axioms of Set Theory we can show the existence of sets that are not measurable, somewhat violating our physical intuition of the notion of length in space. A natural logical question<br />
arises: can some axioms of Set Theory be replaced by different axioms that not only prohibit the existence of the pathological sets just mentioned, but guarantee that every set is measurable? In this talk we will explore this possibility, and in this process we will explain the connection between infinite-length games, sets of real numbers and infinite trees.<br />
This talk is mostly self contained. Only some basic knowledge of Real Analysis will be assumed.<br />
<br />
<br />
----<br />
<br />
<br />
=== Friday, April 12, 2013 at 2:30 pm in VN 116 ===<br />
<br />
==== ''Speaker:'' '''Ryan Lowenstein''', '''Chapman University''' ====<br />
<br />
''Title:'' '''TuringPoint LearningJoint: A Technology Info Session '''<br />
<br />
''Abstract:'' Teaching undergraduates can often be a challenging process, especially if the course is not found to be very interesting by many students (as may be the case with some introductory mathematics courses). Hence, many of us would like to add something to the classroom that could help us improve the engagement of our students (and make math fun again). TurningPoint, a form of clicker technology, does exactly that. This presentation focuses on its effectiveness and will also show you how to get started on your new TurningPoint classroom improvement project.<br />
<br />
<br />
----<br />
<br />
<br />
=== Wednesday, April 3, 2013 at 2:30 pm in VN 116 ===<br />
<br />
==== ''Speaker:'' '''Mustafa Said''', '''University of California, Irvine''' ====<br />
<br />
''Title:'' '''Almost Commuting Matrices'''<br />
<br />
''Abstract:'' We investigate a variant of an old problem in linear algebra and operator theory<br />
that was popularized by Paul Halmos: Must almost commuting matrices be nearly commuting? <br />
To be more precise, we say that a pair of n-by-n complex valued matrices (A, B)<br />
are “almost commuting” if AB − BA is small in some sense. In the same manner, we say<br />
that a pair of n-by-n complex valued matrices (X, Y) are “nearly commuting” if X − A<br />
and Y − B are small in some sense and AB = BA. Although we will be exploring deep<br />
ideas in operator theory, only a basic understanding of undergraduate linear algebra and<br />
real analysis will be assumed. We will briefly discuss history of the problem, discuss the<br />
progress on the problem, and sketch the proof of a quantitative result which establishes that<br />
“almost commuting” matrices are “nearly commuting” for different types of matrices.<br />
<br />
<br />
----<br />
<br />
<br />
=== Wednesday, January 16 -- Wednesday, January 23 2013 ===<br />
<br />
==== 5th Annual CECAT Workshop in Pointfree Mathematics ====<br />
<br />
'''Hosted by the Center of Excellence in Computation, Algebra and Topology (CECAT)'''<br />
<br />
Held at Chapman University, Von Neumann Hall (545 W. Palm Ave, Orange, CA 92866)<br />
<br />
'''Program'''<br />
<br />
'''Wednesday 16th'''<br />
<br />
noon-2pm: '''Open session'''<br />
<br />
'''Thursday 17th'''<br />
<br />
12.30pm-2pm: '''Bernhard Banaschewski'''<br />
<br />
''Title:'' "Regular rings and the PIT"<br />
<br />
'''Friday 18th'''<br />
<br />
noon-1.30pm: '''Bernhard Banaschewski'''<br />
<br />
''Title:'' "On the minimal spectrum of a compact normal frame"<br />
<br />
'''Monday 21st'''<br />
<br />
noon-1.30pm: '''Bernhard Banaschewski'''<br />
<br />
''Title:'' "An example of a pointless countably compact completely regular frame<br />
<br />
2pm-3.30pm: '''Peter Jipsen'''<br />
<br />
''Title:'' "Implementing decision procedures for (generalized) Basic Logic"<br />
<br />
'''Tuesday 22nd'''<br />
<br />
11am-12.30pm: '''Ales Pultr'''<br />
<br />
''Title:'' "Techniques on taking quotients in frames, lattices, quantales etc "<br />
<br />
1pm-2pm '''Joanne Walters-Wayland'''<br />
<br />
''Title:'' "Some comments on Coz and quotients"<br />
<br />
'''Wednesday 23rd'''<br />
<br />
noon-1.30pm: '''Ales Pultr'''<br />
<br />
''Title:'' "Techniques on taking quotients in frames, lattices, quantales etc "<br />
<br />
'''Thursday 24th'''<br />
<br />
11am-12.30pm: '''Bernhard Banaschewski'''<br />
<br />
''Title:'' "Aspects of Strong 0-dimensionality"<br />
<br />
1pm-2.30pm: Drew Moshier<br />
<br />
''Title:'' "An overview of Co-algebras on Compact Regular Spaces"<br />
<br />
'''Friday 25th'''<br />
<br />
noon-1.30pm: '''Bernhard Banaschewski'''<br />
<br />
''Title:'' "Aspects of Strong 0-dimensionality"<br />
<br />
'''Saturday 26th''' <br />
<br />
7pm: '''Cello Concert''' in Von Neumann Hall<br />
<br />
'''[http://mathcs.chapman.edu/CECAT/workshops/CECATworkshop2013schedule.pdf PDF file of the program]'''<br />
<br />
<br />
----<br />
<br />
<br />
=== Wednesday, January 16, 2013 at 4:30 pm in VN ===<br />
<br />
''Speaker:'' '''[http://www.dmu.ac.uk/about-dmu/academic-staff/technology/engineering/scott-linfoot.aspx Dr. Scott Linfoot] of the IEEE and De Montfort University'''<br />
<br />
''Title:'' '''Metadata: Making Molehills out of Mountains'''<br />
<br />
''Abstract:'' This presentation will examine the two prominent media sectors, professional<br />
and consumer, and show that in the near future, the amount of content created<br />
from the consumer space will exceed that created in the professional space.<br />
As a result, there is a vast amount of uncollated and disorganized media moving<br />
around the internet unchecked.<br />
<br />
There is a huge drive at the moment to try to establish some order to what<br />
appears to be a chaotic system. The problem is that using current methods, this<br />
is an extremely time consuming and expensive process. As a result, automatic<br />
metadata generation methods are needed to improve the process<br />
while providing a business case for exploitation.<br />
<br />
This presentation will explore the metadata problem, looking<br />
from the consumer and professional vantage points, and try to<br />
open discussion on how this escalating problem might be averted.<br />
<br />
[http://mathcs.chapman.edu/~jipsen/seminarposters/ScottLinfoot.pdf Poster]<br />
<br />
<br />
<br />
----</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=MathCS_Seminar_2014&diff=10MathCS Seminar 20142021-02-22T18:33:09Z<p>Jipsen: Created page with "== Fall 2014 == === Thursday, December 18th, 2014 at 4pm (tea and cookies at 3:30pm) === ==== ''Speaker:'' '''Lander Cnudde, University of Ghent, Belgium''' ==== ''Title:'..."</p>
<hr />
<div>== Fall 2014 ==<br />
<br />
<br />
=== Thursday, December 18th, 2014 at 4pm (tea and cookies at 3:30pm) ===<br />
<br />
==== ''Speaker:'' '''Lander Cnudde, University of Ghent, Belgium''' ====<br />
<br />
''Title:'' '''Fourier transforms in commutative and non-commutative multicomplex settings'''<br />
<br />
''Abstract:'' This seminar addresses the generalization of the<br />
classical Fourier transform to multicomplex settings. Inspired by a<br />
successful case study on the slices of the non-commutative Clifford<br />
algebra $Cl_{m+1}$, a more conceptual approach to the matter is<br />
established. Using operator relations, we construct a general<br />
background that allows to create Fourier analogues in more general<br />
non-commutative as well as commutative settings. Finally we illustrate<br />
this claim and the underlying line of thoughts by setting up a Fourier<br />
transform for the bicomplex numbers which turns out to be in<br />
accordance to our expectations. The framework uses concepts of both<br />
analysis and algebra, with key roles for the Mehler formula and the<br />
Hille-Hardy formula.<br />
<br />
=== Wednesday December 10th 2014 at 4PM (tea and cookies at 3.30PM) ===<br />
<br />
==== ''Speaker:'' '''Luke Smith, Graduate Student, Department of Mathematics, University of California, Irvine''' ====<br />
<br />
''Title:'' '''Polytope Bounds on Multivariate Value Sets'''<br />
<br />
''Abstract:'' Over finite fields, if the image of a polynomial map is<br />
not the entire field, then its cardinality can be bounded above by a<br />
significantly smaller value. Earlier results bound the cardinality of<br />
the value set using the degree of the polynomial. However, these<br />
bounds can be improved significantly if our bounds depend on the<br />
powers of all monomials in a polynomial map, rather than just the one<br />
with the highest degree. The Newton polytope of a polynomial map is<br />
one such object constructed by each of these monomials, and its<br />
geometry provides sharp upper bounds on the cardinality of the value<br />
set. In this talk, we will explore the geometric properties of the<br />
Newton polytope and show how allows for an improvement on the upper<br />
bounds of the multivariate value set.<br />
<br />
''Bio:'' Luke Smith is a 6th year PhD student at UCI. His research<br />
interests involves number theory, finite fields, value sets, and Witt<br />
vectors. He also enjoys teaching and has recently been involved in<br />
mathematics educational outreach with the UCI Math circle and MIND<br />
Research Institute.<br />
<br />
----<br />
<br />
=== Friday October 24th 2014 at 12.30 (tea and cookies at noon) ===<br />
<br />
==== ''Speaker:'' '''Dr. Brendan Fahy, Postdoctoral Fellow, KEK High Energy Research Organization, Tsukuba, JapanTBA''' ====<br />
<br />
''Title:'' '''Linear combination interpolation, Cuntz relations and infinite products (joint work with I. Lewkowicz, P. Jorgensen and D. Volok)'''<br />
<br />
''Abstract:'' Calculating observable quantities in QCD at low energies<br />
requires a non-perturbative approach. Lattice QCD is a<br />
non-perturbative solution which quantities can be estimates using<br />
Monte Carlo methods. However many quantities such as multi-hadron<br />
operators require large amounts of computational power to<br />
compute. Using the stochastic LapH method the costly matrix inverses<br />
required are estimated rather than computed exactly drastically<br />
reducing the computational costs. These modern computation techniques<br />
allow for the computation of a large number of operators including<br />
multi-hadron operators. Results of the spectrum of energies for the<br />
lowest 50 bound states in a finite box are presented for the rho-meson<br />
channel.<br />
<br />
----<br />
<br />
=== Tuesday October 21st 2014 at 4pm (tea and cookies at 3:30pm) ===<br />
<br />
==== ''Speaker:'' '''Prof. Daniel Alpay, Ben-Gurion University of the Negev, Israel''' ====<br />
<br />
''Title:'' '''Linear combination interpolation, Cuntz relations and infinite products (joint work with I. Lewkowicz, P. Jorgensen and D. Volok)'''<br />
<br />
''Abstract:'' We introduce the following linear combination<br />
interpolation problem: Given $N$ distinct numbers $w_1,..., w_N$ and $N+1$<br />
complex numbers $a_1,..., a_N $and $c$, find all functions f(z) analytic<br />
in a simply connected set (depending on f) containing the points<br />
$w_1,...,w_N$ such that $\sum_{u=1}^N a_u f(w_u)=c$. To this end we prove<br />
a representation theorem for such functions f in terms of an<br />
associated polynomial p(z). We first introduce the following two<br />
operations, substitution of p, and multiplication by monomials $z^j$ ,<br />
$0<= j < N$. Then let M be the module generated by these two operations,<br />
acting on functions analytic near 0. We prove that every function f,<br />
analytic in a neighborhood of the roots of p , is in M. In fact, this<br />
representation of f is unique. To solve the above interpolation<br />
problem, we employ an adapted systems theoretic realization, as well<br />
as an associated representation of the Cuntz relations (from<br />
multi-variable operator theory.) We study these operations in<br />
reproducing kernel Hilbert space): We give necessary and sufficient<br />
condition for existence of realizations of these representation of the<br />
Cuntz relations by operators in certain reproducing kernel Hilbert<br />
spaces, and offer infinite product factorizations of the corresponding<br />
kernels.<br />
<br />
<br />
----<br />
<br />
<br />
=== CECHA Workshop on Integral transforms, boundary values and generalized functions, Fall 2014 ===<br />
Schedule: October 17th - October 21st 2014<br />
<br />
----<br />
<br />
==== Friday October 17th 2014 ==== <br />
Chairperson: Irene Sabadini<br />
<br />
''' 10:50am-11:05am Registration/ Welcome '''<br />
<br />
''' 11:05am-11:55am Michael Shapiro, Instituto Politecnico Nacional, Mexico '''<br />
<br />
Title: “On the Hilbert and Schwarz Formulas and Operators”<br />
<br />
''' 11:55am-12:10pm Discussion Session ''' <br />
<br />
''' 12:20pm-1:30pm Lunch, Athenaeum ''' <br />
<br />
''' 2:00pm-2:50pm Mircea Martin, Baker University ''' <br />
<br />
Title: “Spin Operator Theory”<br />
<br />
''' 2:50pm-3:10pm Discussion Session ''' <br />
<br />
''' 3:10pm-4:00pm M. Elena Luna Elizarraras, Instituto Politecnico Nacional, Mexico ''' <br />
<br />
Title: “A Bicomplex Model of Lobachevsky Geometry”<br />
<br />
''' 4:00pm-4:20pm Discussion Session ''' <br />
<br />
----<br />
<br />
==== Saturday October 18th 2014 ====<br />
<br />
Chairperson: Paula Cerejeiras<br />
<br />
''' 10:00am-10:50am Matvei Libine, Indiana University Bloomington ''' <br />
<br />
Title: "Geometric Properties of Conformal Transformations on $R^{p,q}$"<br />
<br />
''' 10:50am-11:05am Discussion Session ''' <br />
<br />
''' 11:05am-11:55am Ahmed Sebbar, Institut de Mathématiques de Bordeaux ''' <br />
<br />
Title: “Motions of Critical points of Green's functions”<br />
<br />
''' 11:55pm-12:00pm Discussion Session ''' <br />
<br />
''' 12:00pm-1:15pm Lunch, Sandhu ''' <br />
<br />
''' 1:30pm-2:20pm Fabrizio Colombo, Politecnico di Milano, Italy ''' <br />
<br />
Title: “The Fueter-Sce Mapping and its Inverse”<br />
<br />
''' 2:20pm-2:30pm Discussion Session ''' <br />
<br />
''' 2:30pm-3:20pm Adrian Vajiac, Chapman University ''' <br />
<br />
Title: “Multicomplex Hyperfunctions”<br />
<br />
''' 3:20pm-3:30pm Discussion Session ''' <br />
<br />
----<br />
<br />
==== Sunday October 19th 2014 ====<br />
<br />
Chairperson: Mihaela Vajiac<br />
<br />
''' 10:00am-10:50am Irene Sabadini, Politecnico di Milano, Italy ''' <br />
<br />
Title: “Monogenic Hyperfunctions in One and Several Variables”<br />
<br />
''' 10:50am-11:05am Discussion Session ''' <br />
<br />
''' 11:05am-11:55am Uwe Kӓhler, University of Aveiro ''' <br />
<br />
Title: “Crystallographic structures: how to make an effective reconstruction by the spherical X-ray <br />
transform?”<br />
<br />
''' 11:55pm-12:00pm Discussion Session ''' <br />
<br />
''' 12:00pm-1:15pm Lunch, Sandhu ''' <br />
<br />
''' 1:30pm-2:20pm Paula Cerejeiras, University of Aveiro ''' <br />
<br />
Title: “Diffusive Wavelets for Nilpotent Groups”<br />
<br />
''' 2:20pm-2:30pm Discussion Session ''' <br />
<br />
''' 2:30pm-3:20pm Daniel Alpay, Ben-Gurion University of the Negev, Israel ''' <br />
<br />
Title: “Spaces of stochastic (commutative and non commutative) distributions and applications”<br />
<br />
''' 3:20pm-3:30pm Discussion Session ''' <br />
<br />
----<br />
<br />
==== Monday October 20th 2014 ====<br />
<br />
Chairperson: M. Elena Luna Elizarraras<br />
<br />
''' 10:00am-10:50am Craig Nolder, Florida State University ''' <br />
<br />
Title: “Conjugate Harmonic Components of Monogenic Functions and Symmetry”<br />
<br />
''' 10:50am-11:05am Discussion Session ''' <br />
<br />
''' 11:05am-11:55am Graziano Gentili, Università di Firenze ''' <br />
<br />
Title: “Spherical power expansion and a Mittag-Leffler theorem for semi-regular functions”<br />
<br />
''' 11:55am-12:10am Discussion Session ''' <br />
<br />
''' 12:20pm-1:30pm Lunch, Athenaeum ''' <br />
<br />
''' 2:00pm-2:50pm Dana Clahane, Fullerton College ''' <br />
<br />
Title: “Complex, Bicomplex, and Quaternionic Gaussian Moat Problems”<br />
<br />
''' 2:50pm-3:10pm Discussion Session ''' <br />
<br />
''' 3:10pm-4:00pm Lander Cnudde, Universiteit Gent, Belgium ''' <br />
<br />
Title: “Slice Fourier transform: definition, properties and corresponding convolutions”<br />
<br />
''' 4:00pm-4:20pm Discussion Session ''' <br />
<br />
''' 6:30-8:30pm Social Dinner ''' <br />
<br />
----<br />
<br />
==== Tuesday October 21st 2014 ====<br />
<br />
''' 10:00am-12:10pm Discussion Session ''' <br />
<br />
''' 12:20pm-1:30pm Lunch, Athenaeum ''' <br />
<br />
''' 2:00pm-4:00pm Discussion Session ''' <br />
<br />
<br />
<br />
----<br />
<br />
=== Thursday October 9th 2014 at 4pm (tea and cookies at 3:30pm) ===<br />
<br />
==== ''Speaker:'' '''Prof. Ahmed Sebbar, Institut de Mathematiques de Bordeaux''' ====<br />
<br />
''Title:'' '''On a Remarkable Power Series'''<br />
<br />
''Abstract:'' We consider the sequence, defined by<br />
<br />
$s_{2n} = s_{n}, n \geq 1; s_{2n+1} = (-1)^{n}, n \geq 0 $<br />
<br />
or equivalently<br />
<br />
$s_{n} = (-1)^{b} $ if $n=2^a(1+2b); a,b \in \mathbf{N}$<br />
<br />
We explain how it is related to paperfolding and we give a precise analysis at $x = 1$<br />
of the power series<br />
<br />
$f(x) = \sum s_n x^n$<br />
<br />
<br />
----<br />
<br />
=== Thursday, September 25th 2014, at 4pm (tea and cookies at 3:30pm) ===<br />
<br />
==== ''Speaker:'' '''Prof. Christopher Lyon, CalState Fullerton''' ====<br />
<br />
''Title:'' '''Two notions of mirror symmetry for certain K3 surfaces'''<br />
<br />
''Abstract:'' In the mid-1990s, the physicists Berglund and Hubsch<br />
proposed a way to construct a ``mirror partner'' for certain kinds of<br />
Calabi-Yau manifolds. When the manifold has (complex) dimension 2,<br />
these are examples of K3 surfaces. Around the same time, Dolgachev<br />
and others conceived of a version of mirror symmetry that applies to<br />
more general families of K3 surfaces. In this talk, we will introduce<br />
these special kinds of K3 surfaces, which are defined as hypersurfaces<br />
in weighted projective space. Then we will discuss the issue of<br />
compatibility between the aforementioned versions of mirror symmetry.<br />
While the question is open in general, we will highlight a particular<br />
collection of surfaces where the compatibility can be proved. This is<br />
joint work with Paola Comparin, Nathan Priddis, and Rachel Webb.<br />
<br />
----<br />
<br />
=== Thursday, September 11th 2014, 4pm (tea and cookies at 3:30pm) ===<br />
<br />
==== ''Speaker:'' '''Prof. Ahmed Sebbar, Institut de Mathematiques de Bordeaux''' ====<br />
<br />
''Title:'' '''Equivariant functions'''<br />
<br />
''Abstract:'' An equivariant function is a special meromorphic<br />
function on the Poincare upper half-plane. A concrete non trivial<br />
example was given by Don Zagier answering a question of the physicist<br />
Werner Nahm. We show how to construct all the equivariant functions<br />
by using ideas from complex analysis, modular forms and projective<br />
differential geometry. The talk is based on a joint work with<br />
Abdellah Sebbar from The university of Ottawa.<br />
<br />
<!--<br />
----<br />
<br />
== Upcoming Talks and Workshops ==<br />
--><br />
<br />
----<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
=== Wednesday, May 14, 2014 from noon to 12:50 pm in VN 116 ===<br />
<br />
==== ''Speaker:'' '''Dr. Roman Buniy, Chapman University''' ====<br />
<br />
''Title:'' '''Generalized helicity and Beltrami fields'''<br />
<br />
''Abstract:'' We propose covariant and non-abelian generalizations of the magnetic helicity and Beltrami equation. The gauge invariance, variational principle, conserved current, energy-momentum tensor and choice of boundary conditions elucidate the subject. In particular, we prove that any extremal of the Yang-Mills action functional $\frac{1}{4}\int_\Omega{F_{\mu\nu}F^{\mu\nu}}\,d^4x$ subject to the<br />
local constraint $\epsilon^{\mu\nu\alpha\beta}{F_{\mu\nu}F_{\alpha\beta}}=0$ satisfies<br />
the covariant non-abelian Beltrami equation.<br />
<br />
<br />
----<br />
<br />
<br />
=== Thursday, May 8, 2014 from 4pm to 5pm in Von Neumann Hall ===<br />
<br />
==== ''Speaker:'' Dr. Hendrik De Bie, Clifford Research Group, Ghent University, Belgium ====<br />
<br />
''Title:'' '''Convolutions for the quaternion Fourier transform with applications in image processing'''<br />
<br />
''Abstract:'' In this lecture I will explain how a quaternion Fourier<br />
transform may be defined, an how a suitable convolution product can be<br />
associated with it.I will subsequently discuss an application in color image processing,<br />
namely a color edge detector. If time allows, I will also show how some of these results may be<br />
generalized to higher dimensions using Clifford algebras.<br />
<br />
<br />
----<br />
<br />
=== Thursday, April 24, 2014 from 4pm to 5pm in Von Neumann Hall ===<br />
<br />
==== ''Speakers:'' Ryan Burns, Isaac Lien, Scott Lien, David Tyler ====<br />
<br />
''Title:'' '''GrandPAD: Finally technology so easy that it can be used by a people ages 75 to 105.'''<br />
<br />
''Abstract:'' GrandPAD is a technology startup that was born at Chapman that is focused on providing an easy way for seniors citizens over the age of 75 to stay connected with their friends and family. <br />
GrandPAD was founded by Isaac Lien (CIS Major Class of 2017) and Scott Lien (Father of Isaac and former executive with Intuit.) Other key members of the team include Ryan Burns (Computer Science Class of 2014) and David Tyler (Computer Science Class of 2014). <br />
Come and learn about the technology we have used to build GrandPAD and see the product in action. <br />
GrandPAD -- Simply Connected<br />
<br />
See more at: http://www.GrandPAD.net<br />
<br />
<br />
----<br />
<br />
<br />
=== Thursday, April 17, 2014 from 4pm to 5pm in Von Neumann Hall ===<br />
<br />
==== ''Speaker:'' Professor Andrew Moshier, Chapman University ====<br />
<br />
''Title:'' '''String diagrams for categories of posets'''<br />
<br />
''Abstract:'' String diagrams, e.g., for braiding and symmetric monoidal categories, have<br />
proven useful in Physics and Theoretical Computer Science, thanks to coherence<br />
theorems that tell us that diagrams equivalent under suitable topological invariants<br />
denote equal morphisms. In this talk, we extend a similar courtesy to categories of<br />
partially ordered sets by adding an order on diagrams and allowing for topologically<br />
"lossy" diagram rewrites. As an application, we characterize the objects in such<br />
categories that behave as semi-lattices, lattices and distributive lattices.<br />
<br />
<br />
[http://math.chapman.edu/~jipsen/seminarposters/Moshier_PosStrings_20140417.pdf PDF copy] of the abstract containing a diagram.<br />
<br />
<br />
----<br />
<br />
<br />
=== Thursday, April 10, 2014 from 4pm to 5pm in Von Neumann Hall ===<br />
<br />
==== ''Speaker:'' Dr. Ali Nayeri, Chapman University ====<br />
<br />
''Title:'' '''String Gas Cosmology and the Blue Tilt of the Primordial Gravitational Waves'''<br />
<br />
''Abstract:'' The BICEP-2 team has reported the detection of primordial cosmic microwave background B-mode polarization, with hints of a suppression of power at large angular scales relative to smaller scales. Provided that the B-mode polarization is due to primordial gravitational waves, this might imply a blue tilt of the primordial gravitational wave spectrum. Such a tilt would be incompatible with standard inflationary models, although it was predicted some years ago in the context of a mechanism that thermally generates the primordial perturbations through a Hagedorn phase of string cosmology. It has recently been shown that a Hagedorn phase of string gas cosmology can provide a causal mechanism for generating a nearly scale-invariant spectrum of scalar metric fluctuations, without the need for an intervening period of de Sitter expansion.The purpose of this talk is to encourage greater scrutiny of the data with priors informed by a model that is immediately falsifiable, but which predicts features that might be favored by the data-- namely a blue tensor tilt with an induced and complimentary red tilt to the scalar spectrum, with a naturally large tensor to scalar ratio that relates to both.<br />
<br />
<br />
----<br />
<br />
<br />
=== Monday, April 7, 2014 at noon in Von Neumann Hall ===<br />
<br />
==== ''Speaker:'' Dr. Cary Deck, University of Arkansas ====<br />
<br />
''Title:'' '''Behavior in Interconnected Strategic Contests'''<br />
<br />
''Abstract:'' Many strategic situations can be described as a contest where agents make unrecoverable investments in the hope of claiming a prize. This presentation discusses a series of projects where outcomes depend on a set of interconnected contests. One looks at the benefit of alliance formation when there is an opportunistic challenger who can decide which contest to enter. The other considers the case of payoff complementarities across sub-contests. In both cases the comparative statics of the respective model hold in aggregate, however individual behavior systematically differs from what is predicted.<br />
<br />
<br />
----<br />
<br />
<br />
=== Wednesday, March 5, 2014 at noon in Von Neumann Hall ===<br />
<br />
==== ''Speaker:'' Professor Asen Dontchev, University of Michigan, Ann Arbor ====<br />
<br />
''Title:'' '''Inverse Function Theorems: Old and New'''<br />
<br />
''Abstract:'' The classical inverse/implicit function theorems revolves around solving an equation in terms of a parameter and tell us<br />
when the solution mapping associated with this equation<br />
is a differentiable function with respect to the parameter. In this talk we move into a much wider territory in replacing<br />
equation-solving by problems involving nonsmooth equations, as well as<br />
models of optimization, equilibrium, and control theory.<br />
<br />
It turns out that if we put aside differentiability and focus on Lipschitz continuity only,<br />
or even more general metric regularity properties of mappings, we can cover a wider range of models and<br />
get estimates of the solution changes resulting from approximations of the model. As illustrations we<br />
will present implicit function theorems for inequalities and variational inequalities.<br />
<br />
<br />
----<br />
<br />
<br />
=== Thursday, February 27, 2014 from 4pm to 5pm in Von Neumann Hall ===<br />
<br />
==== ''Speaker:'' Professor Michael Campbell from CSUF ====<br />
<br />
''Title:'' '''Phase Transitions in Economic Models: Hot and Cold Market Equilibria in Bounded-Rational Potential Games'''<br />
<br />
''Abstract:'' In economic “games” for which there exists a potential (Shapley & Monderer), a dynamical model for which each agent’s strategy adjustment follows the gradient of the potential (perfectly rational part that wants to maximize payoff) along with a normally distributed random perturbation (part that considers errors in judgment, miscalculations, emotional bias, etc), is shown to equilibrate to a Gibbs measure for a finite number of agents. There is also a non-dynamical way (large deviation theory) to impose this “bounded rationality” using Shannon entropy of agents arbitraging information within the system, and the equilibrium measure is again the Gibbs measure just as in statistical mechanics. For an infinite number of agents, more than one equilibrium measure may occur, which is the analogy of a phase transition in statistical mechanics (similar to water changing to ice or steam). Here, the fluctuation variable that allows us to adjust the influence of the “irrational” element of decisions is related to “temperature” in statistical mechanics. A simple discrete Cournot oligopoly with increased local competition among agents has a phase transition. This model has a rich phase diagram with an "antiferromagnetic" checkerboard state, striped states and maze-like states with varying widths, and finally a "paramagnetic" unordered state. Such phases have economic implications as to how agents compete given various restrictions on how goods are distributed. The standard Cournot model corresponds to a uniform distribution of goods, whereas the power-law variations correspond to goods for which the distribution is more localized.<br />
<br />
<br />
----<br />
<br />
<br />
=== Thursday, January 23 -- Tuesday, January 28, 2014 in Von Neumann Hall ===<br />
<br />
==== 6th Annual CECAT Workshop in Pointfree Mathematics ====<br />
<br />
'''Hosted by the Center of Excellence in Computation, Algebra and Topology (CECAT)'''<br />
<br />
Held at Chapman University, Von Neumann Hall (545 W. Palm Ave, Orange, CA 92866)<br />
<br />
'''Program'''<br />
<br />
'''Thursday 23rd'''<br />
<br />
10.00am-11.30am '''Bernhard Banaschewski'''<br />
<br />
"Further thoughts on Pointfree Function Rings"<br />
<br />
12.30pm-1.30pm '''Fred Dashiell'''<br />
<br />
"A Geometric description of the second dual of C(K)"<br />
<br />
'''Friday 24th'''<br />
<br />
11.30am-12.30pm '''Bernhard Banaschewski'''<br />
<br />
"Further thoughts on Pointfree Function Rings" cont.<br />
<br />
1.00pm-2.00pm '''Peter Jipsen'''<br />
<br />
"Planar (semi) modular lattices"<br />
<br />
'''Saturday 25th'''<br />
<br />
11.30am-1pm '''Mark Sioen'''<br />
<br />
"Some remarks (and more questions) about the topology of uniform convergence on<br />
preferred sublocales "<br />
<br />
'''Monday 27th'''<br />
<br />
noon-1.30pm '''Bernhard Banaschewski'''<br />
<br />
"Archimeadean Kernels and Function Rings"<br />
<br />
2pm-3.30pm '''Drew Moshier'''<br />
<br />
"Gelfand Naimark Duality for Ordered Spaces"<br />
<br />
'''Tuesday 28th'''<br />
<br />
10am-11.30pm '''Bernhard Banaschewski'''<br />
<br />
"Realcompact Alexandroff Frames"<br />
<br />
12.30pm-1.30pm '''Open session'''<br />
<br />
<br />
----<br />
<br />
<br />
=== Monday, January 13, 2014 from 1pm to 2pm in Von Neumann Hall ===<br />
<br />
==== Speaker: Dr. Adrian Nistor, UIUC (now Chapman University) ====<br />
<br />
''Title:'' '''Detecting and Repairing Performance Bugs'''<br />
<br />
''Abstract:'' Software bugs and ineffective testing cost the US economy<br />
tens of billions of dollars each year. My research develops novel<br />
software and hardware techniques for combating software bugs. My<br />
research so far focuses on performance and concurrency bugs.<br />
<br />
In this talk, I will present Toddler and Lullaby, two novel techniques<br />
for automatically detecting and repairing performance<br />
bugs---programming mistakes that slow down program execution. Unlike<br />
profilers, which identify code regions that take a long time to<br />
execute, Toddler and Lullaby focus on execution and code patterns that<br />
are highly indicative of programming mistakes. Toddler and Lullaby<br />
found over 150 new performance bugs in widely used Java and C/C++<br />
applications, including Groovy, Lucene, Google Core Libraries, GCC,<br />
MySQL, and Chromium. Over 100 of these bugs have already been fixed<br />
by developers.<br />
<br />
And 4pm to 5pm in Von Neumann Hall<br />
<br />
''Title:'' '''Detecting Concurrency Bugs'''<br />
<br />
''Abstract:'' Multi-core processors are ubiquitous. To utilize the<br />
processing power of these processors, developers need to write<br />
concurrent code. Unfortunately, writing concurrent code is<br />
notoriously difficult and prone to subtle concurrency bugs. In this<br />
talk, we will review the challenges faced by developers writing<br />
concurrent code and techniques to help developers cope with<br />
concurrency bugs.<br />
<br />
<br />
----</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=MathCS_Seminar_2015&diff=9MathCS Seminar 20152021-02-22T18:32:32Z<p>Jipsen: Created page with " == Fall 2015 == === Thursday, December 10th 2015 at 4pm (tea and cookies at 3:30pm) === ==== ''Speaker:'' '''Dr. Justin Dressel, Chapman University''' ==== ''Title:'' '''..."</p>
<hr />
<div><br />
== Fall 2015 ==<br />
<br />
=== Thursday, December 10th 2015 at 4pm (tea and cookies at 3:30pm) ===<br />
<br />
==== ''Speaker:'' '''Dr. Justin Dressel, Chapman University''' ====<br />
<br />
''Title:'' '''Violating a Hybrid Bell-Leggett-Garg Inequality with Weak Quantum Measurements'''<br />
<br />
''Abstract:'' We discuss both the theoretical background and the<br />
experimental violation of a hybrid Bell-Leggett-Garg inequality using<br />
four superconducting Xmon qubits. The algorithm uses sequential weak<br />
measurements of a Bell state in the form of high-fidelity partial<br />
projections, realized by entangling an ancilla qubit to each data<br />
qubit using a controlled-Z two-qubit gate. After calibration of the<br />
ancilla readout, these partial projections indirectly measure qubit<br />
expectation values with a tunable amount of state disturbance. For<br />
sufficiently weak disturbance, the hybrid inequality can be violated<br />
using all data prepared in a single experimental configuration, thus<br />
avoiding both the fair sampling and the disjoint sampling loopholes<br />
that often appear in traditional Bell inequality implementations.<br />
<br />
----<br />
<br />
=== Wednesday, November 4th 2015 at 4pm in (tea and cookies at 3:30pm) ===<br />
<br />
==== ''Speaker:'' '''Dr. Joshua Sack, California State University Long Beach''' ====<br />
<br />
''Title:'' '''Quantum Logic and Structure'''<br />
<br />
''Abstract:'' This talk presents logics for reasoning about properties of<br />
quantum systems and quantum algorithms. One logic, developed by<br />
Birkhoff and von Neumann, is used to reason about testable properties<br />
of a quantum system; the formal setting is the Hilbert lattice (the<br />
lattice of closed subspaces of a Hilbert space). Another logic is the<br />
logic of quantum actions, developed more recently to reason about the<br />
dynamics of a quantum system; the formal setting here is a quantum<br />
dynamic frame, a kind of labelled transition system often used in<br />
computer science to reason about classical programs. This talk also<br />
explains how these settings are essentially the same via a categorical<br />
duality between the lattices and the frames, and how a decidable<br />
probabilistic extension of the logic of quantum actions can be used to<br />
reason about quantum algorithms such as Grover's search algorithm.<br />
<br />
----<br />
<br />
=== Friday, October 23rd 2015 at noon, Beckman Hall room 107 (no tea and cookies this time, we will be taking the speaker to lunch after) ===<br />
==== ''Speaker:'' '''Prof. Glen van Brummelen, Quest University, Canada''' ====<br />
''Title:'' '''The Mercurial Tale of Spherical Trigonometry'''<br />
<br />
''Abstract:'' The trigonometry we see in high school is merely a pale<br />
reflection of the creative, exciting subject that students learned<br />
only decades ago. Born of the desire to predict the motions of the<br />
heavenly bodies, the trigonometry of ancient astronomers took place<br />
not on a flat sheet of paper, but on the celestial sphere. This led to<br />
a theory with some of the most beautiful results in all of<br />
mathematics, and applications that led to the birth of major modern<br />
developments like symbolic algebra and logarithms. Until the subject<br />
dropped off radar screens after World War II, it continued to enjoy<br />
vitality through applications in navigation and crystallography. The<br />
mathematical path we now travel through high school and college,<br />
heavily emphasizing calculus, unfortunately has deprived students of<br />
other mathematical gems. In this talk, we shall polish some of the<br />
tarnish off one of the brightest of those jewels.<br />
----<br />
=== Friday, October 9th 2015, 2pm (tea and cookies 1:30pm) ===<br />
<br />
==== ''Speaker:'' '''George J. Herrmann, Ph.D. student at University of Denver, Website: http://cs.du.edu/~herrmann''' ====<br />
<br />
''Title:'' '''A tour of Noncommutative Metric Geometry'''<br />
<br />
''Abstract:'' This talk will be an introduction to the area of<br />
Noncommutative Metric Geometry. We will start with discussing<br />
deformation quantization: the history and observations that motivate<br />
our continued interest. We will then shift gears slightly and discuss<br />
some results of Connes and Rieffel in Noncommutative Geometry that<br />
lead to Quantum (Compact) Metric Spaces and quickly introduce a few<br />
nontrivial objects in this category. Then we will end with the work<br />
of Latremoliere in establishing a metric on the category of Quantum<br />
Compact Metric Spaces.<br />
<br />
----<br />
<br />
=== Wednesday, September 30th, 2015, at 3-5pm ===<br />
<br />
==== ''Speaker:'' ''' Professor Daniel Alpay, Earl Katz Chair in Algebraic System Theory, Department of Mathematics, at Ben-Gurion University of the Negev''' ====<br />
<br />
''Title:'' '''Lecture Series by Professor Daniel Alpay, Lectures 5 and 6'''<br />
<br />
''Abstract:'' Rational functions are quotient of polynomials, or<br />
meromorphic functions on the Riemann sphere. Here we consider<br />
matrix-valued rational functions. A number of new aspects (a point can<br />
be at the same time a zero and a pole of the function) and new notions<br />
and methods appear (in particular the state space method. A key role<br />
is played by the realization of a matrix-valued rational function $M$,<br />
say analytic at the origin, that is, its representation in the form<br />
$M(z)=D+zC(I-zA)^{-1}B$, where $A,B,C,D$ are matrices of appropriate<br />
sizes.<br />
<br />
We will discuss matrix-valued rational functions, and their<br />
connections with topics such as complex analysis, interpolation theory<br />
of analytic functions contractive in the open unit disk (Schur<br />
functions), the theory of linear systems (signal processing) and<br />
matrix theory.<br />
<br />
<br />
Lecture 5, 3:00pm-4:00pm<br />
<br />
1) Wavelet filters.<br />
<br />
2) Convex invertible cones.<br />
<br />
3) A new kind of realization.<br />
<br />
<br />
Lecture 6, 4:00pm-5:00pm<br />
<br />
1) Several complex variables.<br />
<br />
2) The non commutative case.<br />
<br />
3) Rational functions on a compact Riemann surface, theta functions.<br />
<br />
4) Quaternionic setting.<br />
<br />
<br />
<br />
----<br />
<br />
=== Tuesday, September 29th, 2015, at 3:30-5:30pm ===<br />
<br />
==== ''Speaker:'' ''' Professor Daniel Alpay, Earl Katz Chair in Algebraic System Theory, Department of Mathematics, at Ben-Gurion University of the Negev''' ====<br />
<br />
''Title:'' '''Lecture Series by Professor Daniel Alpay, Lectures 3 and 4'''<br />
<br />
''Abstract:'' Rational functions are quotient of polynomials, or<br />
meromorphic functions on the Riemann sphere. Here we consider<br />
matrix-valued rational functions. A number of new aspects (a point can<br />
be at the same time a zero and a pole of the function) and new notions<br />
and methods appear (in particular the state space method. A key role<br />
is played by the realization of a matrix-valued rational function $M$,<br />
say analytic at the origin, that is, its representation in the form<br />
$M(z)=D+zC(I-zA)^{-1}B$, where $A,B,C,D$ are matrices of appropriate<br />
sizes.<br />
<br />
We will discuss matrix-valued rational functions, and their<br />
connections with topics such as complex analysis, interpolation theory<br />
of analytic functions contractive in the open unit disk (Schur<br />
functions), the theory of linear systems (signal processing) and<br />
matrix theory.<br />
<br />
<br />
Lecture 3, 3:30pm-4:30pm<br />
<br />
1) Realization and geometry: $J$-unitary rational functions.<br />
<br />
2) Applications to interpolation problems.<br />
<br />
3) Inverse scattering problem (Krein and Marchenko).<br />
<br />
<br />
Lecture 4, 4:30pm-5:30pm<br />
<br />
1) First order degree systems.<br />
<br />
2) Smith-McMillan local form.<br />
<br />
3) Zero-pole structure.<br />
<br />
4) Applications to inverse problems.<br />
<br />
<br />
----<br />
<br />
=== Monday, September 28th 2015 at 4:00pm (tea and cookies at 3:30pm) ===<br />
<br />
==== ''Speaker:'' ''' Prof. Ahmed Sebbar, Bordeaux University, France''' ====<br />
<br />
''Title:'' '''Capacities and Jacobi Matrices'''<br />
<br />
''Abstract:'' Given a system of intervals of the real line, we<br />
construct a Jacobi matrix (tridiagonal and periodic) whose spectrum is<br />
this given system of intervals. We discuss the underlying conditions<br />
and techniques, as well as possible applications.<br />
<br />
----<br />
<br />
=== Friday, September 25th, 2015, at 1-3pm ===<br />
<br />
==== ''Speaker:'' ''' Professor Daniel Alpay, Earl Katz Chair in Algebraic System Theory, Department of Mathematics, at Ben-Gurion University of the Negev''' ====<br />
<br />
''Title:'' '''Lecture Series by Professor Daniel Alpay, Lectures 1 and 2'''<br />
<br />
''Abstract:'' Rational functions are quotient of polynomials, or<br />
meromorphic functions on the Riemann sphere. Here we consider<br />
matrix-valued rational functions. A number of new aspects (a point can<br />
be at the same time a zero and a pole of the function) and new notions<br />
and methods appear (in particular the state space method. A key role<br />
is played by the realization of a matrix-valued rational function $M$,<br />
say analytic at the origin, that is, its representation in the form<br />
$M(z)=D+zC(I-zA)^{-1}B$, where $A,B,C,D$ are matrices of appropriate<br />
sizes.<br />
<br />
We will discuss matrix-valued rational functions, and their<br />
connections with topics such as complex analysis, interpolation theory<br />
of analytic functions contractive in the open unit disk (Schur<br />
functions), the theory of linear systems (signal processing) and<br />
matrix theory.<br />
<br />
<br />
Lecture 1, 1pm-2pm:<br />
<br />
1)Preliminaries on rational functions. Notion of realization.<br />
<br />
2) Transfer functions. Link with linear systems.<br />
<br />
3) Resolvent operators.<br />
<br />
4) Proof of the realization theorem: { The backward-shift realization}.<br />
<br />
5) Various characterizations of rational functions.<br />
<br />
6) The Wiener algebra.<br />
<br />
<br />
Lecture 2, 2pm-3pm:<br />
<br />
1) Main properties of the realization.<br />
<br />
2) Another proof of the realization theorem.<br />
<br />
3) Minimal realization.<br />
<br />
4) Minimal factorizations.<br />
<br />
5) Spectral factorizations.<br />
<br />
6) Reproducing kernel spaces.<br />
<br />
<br />
<br />
<br />
----<br />
<br />
=== Thursday, September 17th, 2015 at 3pm (tea and cookies at 2:30pm) ===<br />
<br />
==== ''Speaker:'' '''Prof. Ahmed Sebbar, Bordeaux University, France''' ====<br />
<br />
''Title:'' ''' The Frobenius determinant theorem and applications.'''<br />
<br />
''Abstract:'' In this first talk, we will discuss the celebrated determinant<br />
Frobenius theorem and how it arised naturally in the study of a<br />
hierarchy of hypersurfaces, of partial differential operators and<br />
metrics.<br />
<br />
The first elements of this hierarchy are the cubic $x^3 + y ^3 + z^3 -<br />
3xyz = 1$ (so called Jonas hexenhut) and the partial differential<br />
operator $\Delta_3 = \frac{\delta^3}{\delta_{x^3}} +<br />
\frac{\delta^3}{\delta_{y^3}} + \frac{\delta^3}{\delta_{z^3}} -3<br />
\frac{\delta^3}{\delta_x \delta_y \delta_z}$, introduced by P.Humbert<br />
in 1929 in another context. We explain why this operator is a good<br />
extension to ${\rm I\!R}^3$ of the Laplacian in two dimensions<br />
$\Delta_2 = \frac{\delta^2}{\delta_{x^2}} +<br />
\frac{\delta^2}{\delta_{y^2}}$ We discuss its links with Spectral<br />
theory, Elliptic functions, number theory and a sort of Finsler<br />
geometry.<br />
<br />
This is a part of a large project conducted in collaboration with<br />
Daniele Struppa, Adrian Vajiac and Mihaela Vajiac.<br />
<br />
----<br />
<br />
=== Thursday, September 3rd, 2015 at 4pm (tea and cookies at 3:30pm) ===<br />
<br />
==== ''Speaker:'' '''Prof. Yasushi Kondo, Kinki University, Osaka, Japan''' ====<br />
<br />
''Title:'' '''Composite Quantum Gates with Aharanov–Anandan phases.'''<br />
<br />
''Abstract:'' Unitary operations acting on a quantum system must be<br />
robust against systematic errors in control parameters for reliable<br />
quantum computing. Composite pulse technique in nuclear magnetic<br />
resonance realizes such a robust operation by employing a sequence of<br />
possibly poor-quality pulses. We show that composite pulses that<br />
compensate for a pulse length error in a one-qubit system have a<br />
vanishing dynamical phase and thereby can be seen as geometric quantum<br />
gates with Aharanov-Anandan phases.<br />
<br />
== Spring 2015 ==<br />
<br />
<br />
<br />
=== Friday, February 13th, 10:00 a.m. to noon ===<br />
<br />
==== ''Speaker:'' '''Professor Daniel Alpay, Earl Katz Chair in Algebraic System Theory, Department of Mathematics, at Ben-Gurion University of the Negev''' ====<br />
<br />
''Title:'' '''Fock spaces and non commutative stochastic distributions. The free setting. Free (non commutative) stochastic processes.'''<br />
<br />
''Abstract:'' We present the non commutative counterpart of the<br />
previous talk. We will review the main definitions of free analysis<br />
required and then present, and build stationary increments non<br />
commutative processes. The values of their derivatives are now<br />
continuous operators from the space of non commutative stochastic test<br />
functions into the space of non commutative stochastic distributions.<br />
<br />
More details at:<br />
<br />
http://blogs.chapman.edu/scst/2015/02/02/daniel-alpay/<br />
<br />
----<br />
<br />
=== Thursday, February 12th, 11:00 a.m. to 1:00 p.m. ===<br />
<br />
==== ''Speaker:'' '''Professor Daniel Alpay, Earl Katz Chair in Algebraic System Theory, Department of Mathematics, at Ben-Gurion University of the Negev''' ====<br />
<br />
''Title:'' '''Bochner and Bochner-Minlos theorem. Hida’s white noise space and Kondratiev’s spaces of stochastic distributions, Stationary increments stochastic processes. Linear stochastic systems.'''<br />
<br />
''Abstract:'' We discuss the Bochner-Minlos theorem and build Hida’s<br />
white noise space. We build stochastic processes in this space with<br />
derivative in the Kondratiev space of stochastic distributions. This<br />
space is an algebra with the Wick product, and its structure of<br />
tallows to define stochastic integrals.<br />
<br />
More details at:<br />
<br />
http://blogs.chapman.edu/scst/2015/02/02/daniel-alpay/<br />
<br />
----<br />
<br />
=== Tuesday, February 10th, 10:00 a.m. to noon ===<br />
<br />
==== ''Speaker:'' '''Professor Daniel Alpay, Earl Katz Chair in Algebraic System Theory, Department of Mathematics, at Ben-Gurion University of the Negev''' ====<br />
<br />
''Title:'' '''Positive definite functions, Countably normed spaces, their duals and Gelfand triples'''<br />
<br />
''Abstract:'' We survey the notion of positive definite functions and<br />
of the associated reproducing kernel Hilbert spaces. Examples are<br />
given relevant to the sequel of the talks. We also define nuclear<br />
spaces and Gelfand triples, and give as examples Schwartz functions<br />
and tempered distributions.<br />
<br />
More details at:<br />
<br />
http://blogs.chapman.edu/scst/2015/02/02/daniel-alpay/<br />
<br />
----<br />
<br />
<br />
=== Wednesday, January 14th, 2015 at 3pm (tea and cookies at 2:30pm) ===<br />
<br />
==== ''Speaker:'' '''Prof. Richard N. Ball, University of Denver''' ====<br />
<br />
''Title:'' '''Pointfree Pointwise Suprema in Unital Archimedean L-Groups (joint work with Anthony W. Hager, Wesleyan University, and Joanne Walters-Wayland, Chapman University)'''<br />
<br />
''Abstract:'' When considering the suprema of real-valued functions,<br />
it is often important to know whether this supremum coincides with the<br />
function obtained by taking the supremum of the real values at each<br />
point. It is therefore ironic, if not surprising, that the fundamental<br />
importance of pointwise suprema emerges only when the ideas are placed<br />
in the pointfree context.<br />
<br />
For in that context, namely in $\mathcal{R}L$, the archimedean<br />
$\ell$-group of continuous real valued functions on a locale $L$, the<br />
concept of pointfree supremum admits a direct and intuitive<br />
formulation which makes no mention of points. The surprise is that<br />
pointwise suprema can be characterized purely algebraically, without<br />
reference to a representation in some $\mathcal{R}L$. For the<br />
pointwise suprema are precisely those which are context-free, in the<br />
sense of being preserved by every $W$-morphism out of $G$.<br />
<br />
(The algebraic setting is the category $W$ of archimedean<br />
lattice-ordered groups (`$\ell$-groups) with designated weak order<br />
unit, with morphisms which preserve the group and lattice operations<br />
and take units to units. This is an appropriate context for this<br />
investigation because every $W$-object can be canonically<br />
represented as a subobject of some $\mathcal{R}L$.)<br />
<br />
Completeness properties of $\mathcal{C}X$ with respect to (various<br />
types of) bounded suprema are equivalent to (various types of)<br />
disconnectivity properties of $X$. These are the classical<br />
Nakano-Stone theorems, and their pointfree analogs for $\mathcal{R}L$<br />
are the work of Banaschewski and Hong. We show that every bounded<br />
(countable) subset of $\mathcal{R}^+L$ has a join in $\mathcal{R}L$<br />
iff $L$ is boolean (a $P$-frame). More is true: every existing<br />
bounded (countable) join of an arbitrary $W$-object $G$ is<br />
pointwise iff the Madden frame $\mathcal{M}G$ is boolean (a<br />
$P$-frame).<br />
<br />
Perhaps the most important attribute of pointwise suprema is that<br />
density with respect to pointwise convergence detects epicity. We<br />
elaborate. Of central importance to the theory of $W$ is<br />
its smallest full monoreflective subcategory $\beta{}W$,<br />
comprised of the objects having no proper epic extensions. That means<br />
each $W$-object $G$ has a largest epic extension $G \to<br />
\beta G$, and this extension is functorial. It turns out that a<br />
$W$-extension $A \leq B$ is epic iff $A$ is pointwise dense<br />
in $B$. Thus the epireflective hull $\beta G$ of an arbitrary<br />
$W$-object $G$ can be constructed by means of pointwise<br />
Cauchy filters.</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=MathCS_Seminar_2016&diff=8MathCS Seminar 20162021-02-22T18:31:48Z<p>Jipsen: Created page with " == Fall 2016 == The seminar talks are in Von Neumann Hall VN 116 (545 W Palm Ave corner of W Palm Ave and railroad, Orange, CA 92866). See [http://www.chapman.edu/discover/..."</p>
<hr />
<div><br />
== Fall 2016 ==<br />
<br />
The seminar talks are in Von Neumann Hall VN 116 (545 W Palm Ave<br />
corner of W Palm Ave and railroad, Orange, CA 92866).<br />
<br />
See [http://www.chapman.edu/discover/maps-directions/index.aspx Maps<br />
and directions], Von Neumann Hall is Building 38 on the<br />
[http://www.chapman.edu/about/_files/maps-and-directions/current-maps/campus-map.pdf<br />
Campus Map]<br />
<br />
<!--'''Note:''' This semester we will (for now) start talks '''at 1:15<br />
pm'''. From 12:45 pm to 1:15 pm is time for refreshments and<br />
interesting conversations with the speaker, so consider coming a bit<br />
early.--><br />
<!--<br />
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<br />
== Upcoming Talks and Workshops ==<br />
--><br />
<br />
<br />
<br />
<br />
<br />
----<br />
<br />
=== Thursday, December 15th at 4:00pm (tea and cookies at 3:30pm) ===<br />
<br />
==== ''Speaker:'' '''Alexander Kurz, University of Leicester''' ====<br />
<br />
''Title:'' '''Reasoning in Applied Logics'''<br />
<br />
''Abstract: '' Reasoning is a fundamental challenge in many areas of Computer Science such as databases (query-answering), semantic web (ontologies), artifical ingelligence (planning), and software engineering (formal methods, verification). But reasoning in general purpose logics such as first-order predicate logic does not lend itself well to automatisation. Over the decades, this lead to the succesful development of a multitude of bespoke logics, each tailored to a specific application (time, knowledge, obligations, probabilities, dynamics, …).<br />
With the growing success of these logics applications are getting more ambitious and require reasoning methods for combinations of such logics. In this talk, we present an approach that aims at designing good proof systems for a wide variety of logics based on so-called multi-type display calculi. We will also report on our work of building tools that support reasoning about and in such calculi.<br />
<br />
<br />
<br />
----<br />
<br />
=== Thursday, December 8th at 4:00pm (tea and cookies at 3:30pm) ===<br />
<br />
==== ''Speaker:'' '''Dr. Michael Campbell, CSUF''' ====<br />
<br />
''Title:'' '''The Statistical Mechanics of Bounded-Rational Potential Games with Applications'''<br />
<br />
''Abstract: '' Frequently, real economic agents do not follow purely rational strategies. These individual non-rational behaviors (due to errors in judgment, incomplete information, emotional bias, etc.) can result in some fascinating organized large-scale structures, which depend on the degree of non-rational behavior.<br />
<br />
We look at two such models for Potential Games [Shapley and Monderer]: a dynamical drift-diffusion model, and a static large deviation theory model based on Shannon information entropy and arbitrage. The equilibrium measure in both cases is the Gibbs measure found in statistical mechanics. We show that the variables that gauge non-rational behavior in both models are related to “temperature” by a fluctuation-dissipation relation.<br />
<br />
A type of localized discrete Cournot oligopoly has a rich phase diagram with an "antiferromagnetic" checkerboard state, striped states and maze-like states with varying widths, and finally a "paramagnetic" unordered state. Such phases have economic implications as to how agents compete given various restrictions on how goods are distributed. <br />
<br />
The theory is also applied to a Speculative and Hedging Model in Oil and U.S. Dollar Markets [Carfi and Musolino] for a single multinational “airline” and many “bank” players. Based on results for the Nash equilibrium (zero temperature) and preliminary results, there is a phase transition for which a single equilibrium exists at higher non-rational behavior (high temperature), and two equilibria at lower non-rational behavior (low temperature), when the “airline” makes no purchase of oil. The low temperature phase is in the spirit of the Sonnenschein–Mantel–Debreu theorem, with the extra insight of symmetry-breaking to explain multiple equilibria. Likewise, Huw Dixon’s result on the “inevitability of collusion” is shown to hold for a Cournot oligopoly with a Veblen good. Purely rational neoclassical theory (i.e., Nash equilibrium analysis) alone does not predict this, even though it is observed to occur in more general cases.<br />
<br />
<br />
----<br />
<br />
=== Tuesday, December 6th at 4:00pm (tea and cookies at 3:30pm) ===<br />
<br />
==== ''Speaker:'' '''Professor Alain Yger, IMB, Universit ́e de Bordeaux, Talence, France''' ====<br />
<br />
''Title:'' '''An arithmetic elimination theorem and bounds for multivariate residues'''<br />
<br />
''Abstract: '' I will present an elimination theorem inspired by a classical theorem of Oskar Perron, combined with the approach proposed in 2005 by Zbigniew Jelonek towards the sharp geometric effectiveness of Hilbert’s Nullstellensatz. I will show next how it can be used in order to get precise estimates (in terms of the geometric and arithmetic complexity of all the data, fitting with both geometric and arithmetic B ́ezout theorems) for total sums of multivariate residues related to polynomials maps defined over Q over an algebraic variety also defined over Q. Methods start with revisiting Euclid’s algorithm, together with Bergman-Weil developments. This is very recent joint work with Mart ́ın Sombra (ICREA and University of Barcelona). <br />
<br />
<br />
----<br />
<br />
=== Thursday, December 1st at 4:00pm (tea and cookies at 3:30pm) ===<br />
<br />
==== ''Speaker:'' '''Prof. Herbert W. Hamber, University of California at Irvine''' ====<br />
<br />
''Title:'' '''The Problem with Quantum Gravitation'''<br />
<br />
''Abstract: '' Of the four fundamental forces, Gravity is the one that has been studied the longest. Besides being an immediate fact of everyday life, it still presents us today with some of the deepest challenges in contemporary physics. Einstein’s (classical) relativistic Gravity is unique, in the sense that it influences both the very largest and the very smallest length scales. These include black holes, pulsars, quasars, the Big Bang, and the Universe as a whole, at one end of the spectrum, and the microscopic structure of space-time and unified theories at the other end. Moreover, one of its most basic predictions (gravitational waves) has recently been detected on earth.<br />
Recent attempts at a quantum theory of Gravity have tried to combine, in a consistent framework, what some have regarded as the two greatest achievements of 20-th century physics: General Relativity and Quantum Mechanics. A major challenge has been to develop specific predictions that might be tested by observation. The aim of my talk will be to give a very broad brush (and hopefully elementary) survey of our understanding of Gravity and its Quantum extension.<br />
<br />
<br />
<br />
----<br />
<br />
=== Thursday, November 17th at 4:15pm (tea and cookies at 3:45pm) ===<br />
<br />
==== ''Speaker:'' '''Prof. Daniel Alpay, Chapman University''' ====<br />
<br />
''Title:'' '''Linear stochastic systems, commutative and non commutative: a white noise space approach'''<br />
<br />
''Abstract: '' The Gelfand triple consisting of the Schwartz functions the Lebesgue space and tempered distributions play a key role in analysis, and in particular in the theory of partial differential equations. We describe related triples, where the Lebesgue space is replaced by the symmetric (resp. full) Fock space associated to the Lebesgue space. The term "white noise space" in the title refers to Hida's white noise space, which is a construction of the symmetric Fock space associated to the Lebesgue space using the Bochner-Minlos theorem. The tempered distributions are now replaced by spaces of stochastic distributions. These are instances of a new family of topological algebras, which generalizes the notion of Banach algebra.<br />
As applications we study stationary increments stochastic processes and their derivatives, stochastic calculus, and linear stochastic systems, where randomness is also in the parameters of the system.<br />
<br />
The talk is based on joint works with Haim Attia, Palle Jorgensen, Alon Kipnis, David Levanony, Ariel Pinhas, and Guy Salomon. <br />
<br />
<br />
<br />
<br />
<br />
----<br />
<br />
=== Thursday, November 10th at 4:15pm (tea and cookies at 3:45pm) ===<br />
<br />
==== ''Speaker:'' '''Prof. Matthew Leifer, Chapman University''' ====<br />
<br />
''Title:'' '''Plausibility Measures on Test Spaces'''<br />
<br />
''Abstract: '' Plausibility measures are structures for reasoning in the face of uncertainty that generalize probabilities, unifying them with weaker structures like possibility measures and comparative probability relations. So far, the theory of plausibility measures has only been developed for classical sample spaces, but there are various reasons for<br />
wanting to apply them to quantum theory, as I shall explain. In this talk, I will generalize the theory to test spaces, so that plausibility<br />
measures can be applied to general operational theories, and to quantum theory in particular. Our main results are on when a plausibility<br />
measure agrees with a probability measure, i.e. when its comparative relations coincide with those of a probability measure. For strictly<br />
finite test spaces we obtain a precise analogue of the classical result that the Archimedean condition is necessary and sufficient for agreement<br />
between a plausibility and a probability measure. In the locally finite case, the Archimedean condition implies the weaker condition of almost<br />
agreement, and one needs a stronger version of the Archimedean condition to get agreement. This is the same as the condition needed in the<br />
classical measure-theoretic case, even though we are only dealing with tests with a finite number of outcomes.<br />
<br />
This talk is based on joint work with Tobias Fritz (preprint available at: https://arxiv.org/abs/1505.01151 )<br />
<br />
<br />
<br />
----<br />
<br />
=== CECHA Conference: Friday to Monday, November 4th to November 7th in Sandhu Conference Center ===<br />
<br />
==== ''Speaker:'' '''CECHA: Celebrating Daniel Alpay’s 60th birthday''' ====<br />
<br />
''Title:'' '''International Conference on Complex Analysis and Operator Theory'''<br />
<br />
''Abstract: '' For directions, schedule, and book of abstracts, see CECHA Webpage: [http://www.chapman.edu/scst/research/centers-of-excellence/cecha/index.aspx CECHA Webpage],<br />
<br />
<br />
<br />
----<br />
<br />
=== Thursday, October 27th at 4pm (tea and cookies at 3:30pm) ===<br />
<br />
==== ''Speaker:'' '''Prof. Roman Buniy, Chapman University''' ====<br />
<br />
''Title:'' '''Geometric invariants associated with linear transformations'''<br />
<br />
''Abstract: '' Invariant operators associated with linear transformations naturally lead to invariant differential forms and related geometric invariants.<br />
Complex analytic properties of transformations provide an efficient way to generate and compute the invariants.<br />
<br />
<br />
<br />
----<br />
<br />
=== Thursday, October 20th at 4pm (tea and cookies at 3:30pm) ===<br />
<br />
==== ''Speaker:'' '''Christopher Cantwell, USC''' ====<br />
<br />
''Title:'' '''Quantum Chess, Making Quantum Phenomena Accessible'''<br />
<br />
''Abstract: '' Quantum phenomena have remained largely inaccessible to the general public. There tends to be a scare factor associated with the word “Quantum”, with the usual responses being along the lines of “too complicated for me.” This is in large part due to the alien nature of phenomena such as superposition and entanglement. However, Quantum Computing is a very active area of research and one day we will have games that run on those quantum computers. Quantum phenomena such as superposition and entanglement will seem as normal as gravity. Is it possible to create such games today? Can we make games that are built on top of a realistic quantum simulation and introduce players of any background to quantum concepts in a fun and mentally stimulating way?<br />
<br />
On of the difficulties with any quantum simulation run on a classical computer is that the Hilbert space grows exponentially, making simulations of an appreciable size physically impossible due largely to memory restrictions. Here we will discuss the conception and development of Quantum Chess, and how to overcome some of the difficulties faced. We can then ask the question, “What’s next?” What are some of the difficulties Quantum Chess still faces, and what is the future of quantum games?<br />
<br />
<br />
----<br />
<br />
=== Thursday, October 13th at 4pm (tea and cookies at 3:30pm) ===<br />
<br />
==== ''Speaker:'' '''N.D. Hari Dass, Tata Centre for Interdisciplinary Sciences, Tata Inst. for Fundamental Research (TIFR-TCIS), Hyderabad, India''' ====<br />
<br />
''Title:'' '''Three results on weak measurements'''<br />
<br />
''Abstract: '' I shall present three important results on weak measurements.<br />
They are: <br />
i) repeated weak measurements on a single copy can not provide any information on it and further that in the limit of very large such mea- surements, weak measurements have exactly the same characterstics as strong measurements.However, a number of interesting results can be obtained for joint probabilities for the random walks in the quantum state space under such repeated weak measurements, <br />
ii) the apparent non-invasiveness of weak measurements is no more advantageous than strong measurements in the spe- cific context of Leggett-Garg measurements when errors are properly taken into account and finally, iii) weak value measurements are optimal, in the precise sense of Wootters and Fields, when the post-selected states are mu- tually unbiased with respect to the eigenstates of the observable whose weak values are being measured. Furthermore, notion of weak value coordinates for state spaces are introduced and elaborated. <br />
It is shown that the metric on the state space in these coordinates is conformal.<br />
<br />
<br />
----<br />
<br />
=== Thursday, October 6th at 4pm (tea and cookies at 3:30pm) ===<br />
<br />
==== ''Speaker:'' '''Prof. Ahmed Sebbar, Bordeaux University ''' ====<br />
<br />
''Title:'' '''Differentially algebraic functions '''<br />
<br />
''Abstract: '' We call an analytic function f(z), defined on some open subset Differentially Algebraic (DA) if it satisfies some differential equation of the form Q(z, f(z), f'(z),\cdots, f^{(n)}(z)) = 0 for all z in its domain, where Q is a nonzero polynomial of n+2 variables, with complex coefficients.The four functions: The exponential functions e^z, the Euler Gamma function Gamma(z), the Riemann Zeta function zeta(s) and the Jacobi theta function theta(tau) are all related by Mellin transformations.<br />
<br />
We explain briefly why Gamma and zeta are not DA but the function theta verifies a nonlinear differential equation of the third order. We give various reasons (Geometry, Arithmetics, Dynamical Systems… ) as to why this equation must exist.<br />
<br />
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<br />
=== Thursday, September 22nd at 4pm (tea and cookies at 3:30pm) ===<br />
<br />
==== ''Speaker:'' '''Dr. Josh Mutus from Google, Santa Barbara ''' ====<br />
<br />
''Title:'' '''What we do at the Google Quantum Hardware team'''<br />
<br />
''Abstract: '' We’re trying to build a quantum computer capable of serving Google’s billions of users worldwide. I’ll introduce why Google wants to build a quantum computer and outline our two major thrusts: quantum annealing and error-corrected universal quantum computation. I’ll describe how we’re building our quantum computer from the ground up, starting with the microfabrication techniques used to engineer our superconducting qubits. Also, I’ll share overview of our new Quantum Hardware lab, including specialized high-capacilty cryostats, custom built high-frequency electronics and a our stack of open-source experimental control software.<br />
<br />
Josh works with the team of Dr. John Martinis, who heads a cutting-edge experimental program for realizing a quantum computer with superconducting quantum bits. You can read about some of their recent accomplishments here: http://web.physics.ucsb.edu/~martinisgroup/<br />
<br />
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<br />
=== Thursday, September 15th at 4pm (tea and cookies at 3:30pm) ===<br />
<br />
==== ''Speaker:'' '''Prof. Ali Nayeri, Chapman University ''' ====<br />
<br />
''Title:'' '''Truly quantum Gibbs: Thermal state of a system whose charges don’t commute '''<br />
<br />
''Abstract: '' I present a detailed analysis for the classical stability of $4$<br />
dimensional Anti-de Sitter spacetime (AdS$_4$) by decomposing the<br />
first-order perturbations of a spherical symmetric gravitational<br />
field into so called tensor harmonics which transform as<br />
irreducible representative of the rotation group (Regge-Wheeler<br />
decomposition). It is shown that there is no nontrivial<br />
stationary perturbation for the angular momentum $l < 2$. The<br />
stability analysis forces the frequency of the gravitational modes<br />
to be constrained in a way that the frequency of scalar modes are<br />
constrained.<br />
<br />
----<br />
<br />
=== CECHA Workshop: Monday to Monday, August 22nd to August 29th at 9am (tea and cookies at 8:30am) ===<br />
<br />
==== ''Speaker:'' '''Professor Takashi Aoki, Kindai University''' ====<br />
<br />
''Title:'' '''Operators of infinite order and exact WKB analysis'''<br />
<br />
''Abstract: '' Contents and Description:<br />
Part I Differential operators, microdifferential operators and pseudodifferential operators of infinite order<br />
1. Introduction<br />
2. Algebraic definitions of pseudodifferential operators in complex analytic category<br />
3. Kernel functions<br />
4. Symbols of pseudodifferential operators and symbolic calculus<br />
5. Exponential calculus<br />
6. Applications<br />
<br />
Part II Exact WKB analysis<br />
1. Introduction<br />
2. WKB solutions of ODE of second order with a large parameter<br />
3. Borel sums of WKB solutions and connection formulas<br />
4. WKB solutions and microdifferential operators<br />
5. Higher-order equations and infinite-order equations<br />
6. Applications to special functions<br />
<br />
Prerequisites for this lecture are complex function theory and ordinary differential equations in the complex domain.<br />
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<br />
=== Friday, August 26th at 11am (tea and cookies at 10:30am) ===<br />
<br />
==== ''Speaker:'' '''Nicole Yunger Halpern (Institute for Quantum Information and Matter, California ''' ====<br />
<br />
''Title:'' '''Truly quantum Gibbs: Thermal state of a system whose charges don’t commute '''<br />
<br />
''Abstract: '' The grand canonical ensemble lies at the core of statistical mechanics. A small system thermalizes to this state while exchanging heat and particles with a bath. A quantum system may exchange quantities, or “charges,” represented by operators that fail to commute. Whether such a system thermalizes, and what form the thermal state has, concerns truly quantum thermodynamics. I characterize this state in three ways: First, I generalize the system-and-bath microcanonical ensemble. Tracing out the bath yields the system’s thermal state. Second, this thermal state is expected to be the fixed point of typical dynamics. Finally, the thermal state is completely passive (unable to output thermodynamic work) in a resource-theory model for thermodynamics. This study opens new avenues into equilibrium in the presence of quantum noncommutation. <br />
References:<br />
Yunger Halpern et al. Nature Communications 7, 12051 (2016). Yunger Halpern arXiv:1409.7845 (2014). <br />
This work was conducted with Philippe Faist, Jonathan Oppenheim, and Andreas Winter. <br />
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<br />
<br />
=== Tuesday, August 23rd at 11am (tea and cookies at 10:30am) ===<br />
<br />
==== ''Speaker:'' '''Professor Howard Wiseman of Griffith University, and the Centre for Quantum Computation and Communication Technology''' ====<br />
<br />
''Title:'' '''Quantum State Smoothing - what does an open quantum system do when it is only partly observed? (by Howard Wiseman and Ivonne Guevara)'''<br />
<br />
''Abstract: '' Under noisy observations, estimation theory allows one to infer the state of the measured system, if its a priori statistics are given. In the continuous time situation, three different types of estimation can be distinguished: filtering, which is estimating of the state at time t from earlier records; retro-filtering, which is estimating the state at time t from later records; and smoothing, which is estimating the state at time t from both earlier and later records. Of the three, smoothing allows the greatest precision. This theory has been well developed in classical systems, but its application to quantum systems has only recently begun to be explored. Previous works have used the term “quantum smoothing” to mean estimating classical parameters, [Tsang, Phys. Rev. Lett. 102, 250403 (2009)], which is essentially classical smoothing in which the noisy observation of the classical parameters is mediated by a quantum system. Here we introduce quantum state smoothing, where the state of a partially observed open quantum system itself is smoothed [Guevara and Wiseman, Phys. Rev. Lett. 115, 180407 (2015).]. We achieve this by applying classical smoothing to a hypothetical unobserved noisy measurement record correlated with the stochastic dynamics ("quantum trajectories") of the system, induced by that hypothetical measurement. Using the formalism of linear quantum trajectories, we simulate quantum state smoothing for a qubit, and quantify how well the unobserved results can be estimated. Our investigations shed new light on the nature of the quantum state. <br />
----<br />
<br />
=== Thursday, August 18th at 4:00pm (tea and cookies at 3:30pm) ===<br />
<br />
==== ''Speaker:'' '''Professor Fabrizio Colombo, Politecnico di Milano''' ====<br />
<br />
''Title:'' '''Quaternionic spectral theory'''<br />
<br />
''Abstract:'' In this talk we give an overview of the quaternionic spectral theory based on the notion of S-spectrum. We present the state of the art of the quaternionic version of the various functional calculi associated with slice hyperholomorphic functions. Moreover we discuss the spectral theorem for quaternionic (unbounded) normal operators using the notion of S-spectrum. The proof consists of first establishing a spectral theorem for quaternionic bounded normal operators and then using a transformation which maps a quaternionic unbounded normal operator to a quaternionic bounded normal operator. With the spectral theorem we complete the foundation of spectral analysis of quaternionic operators. An important motivation for studying the spectral theorem for quaternionic unbounded normal operators is given by the subclass of unbounded anti-self adjoint quaternionic operators which plays a crucial role in the quaternionic quantum mechanics.<br />
----<br />
<br />
<br />
----<br />
<br />
== Spring 2016 ==<br />
<br />
The seminar talks are in Von Neumann Hall VN 116 (545 W Palm Ave<br />
corner of W Palm Ave and railroad, Orange, CA 92866).<br />
<br />
See [http://www.chapman.edu/discover/maps-directions/index.aspx Maps<br />
and directions], Von Neumann Hall is Building 38 on the<br />
[http://www.chapman.edu/discover/_files/CU_CampusMap2012-13-2.pdf<br />
Campus map]<br />
<br />
<!--'''Note:''' This semester we will (for now) start talks '''at 1:15<br />
pm'''. From 12:45 pm to 1:15 pm is time for refreshments and<br />
interesting conversations with the speaker, so consider coming a bit<br />
early.--><br />
<!--<br />
----<br />
<br />
== Upcoming Talks and Workshops ==<br />
--><br />
<br />
<br />
----<br />
<br />
=== Thursday, May 19th at 4pm (tea and cookies at 3:30pm) ===<br />
<br />
==== ''Speaker:'' '''Professor Marco Panza, Professor of Philosophy at Universite Paris 1 (Sorbonne)''' ====<br />
<br />
''Title:'' '''Platonisms (in Philosophy of Mathematics) '''<br />
<br />
Abstract: Platonism is a very often mentioned option in the discussion about the foundation and methodology of mathematics, but it encompasses quite different conceptions. In my talk, I will try to present an overview of different platonist views in contemporary (and less contemporary) philosophy of mathematics.<br />
<br />
<br />
----<br />
<br />
=== Wednesday, April 27th at 12noon (tea and cookies at 11:30am) ===<br />
<br />
==== ''Speaker:'' '''Alessandra Palmigiano, TU Delft, The Netherlands''' ====<br />
<br />
''Title:'' '''Algorithmic correspondence and canonicity for non-distributive logics'''<br />
<br />
''Abstract:'' Since the 1970s, correspondence theory has been one of the most important items in the toolkit of modal logicians. Unified correspondence [6] is a very recent approach, which has imported techniques from duality, algebra and formal topology [10] and exported the state of the art of correspondence theory well beyond normal modal logic, to a wide range of logics including, among others, intuitionistic and distributive lattice-based (normal modal) logics [8], non-normal (regular) modal logics [17], substructural logics [9, 7, 5], hybrid logics [13], and mu-calculus [2, 4, 3].<br />
<br />
The breadth of this work has stimulated many and varied applications. Some are closely related to the core concerns of the theory itself, such as the understanding of the relationship between different methodologies for obtaining canonicity results [16, 7], or of the phenomenon of pseudo-correspondence [11]. Other, possibly surprising applications include the dual characterizations of classes of finite lattices [14], the identification of the syntactic shape of axioms which can be translated into analytic rules of a proper display calculus [15], and the design of display-type calculi for the logics of capabilities and resources, and their applications to the logical modelling of business organizations [1]. Finally, the insights of unified correspondence theory have made it possible to determine the extent to which the Sahlqvist theory of classes of normal DLEs can be reduced to the Sahlqvist theory of normal Boolean expansions, by means of Gödel-type translations [12]. It is interesting to observe that, through the development of applications such as [16, 15, 11], the algorithm ALBA acquires novel conceptual significance, which cannot be reduced exclusively to its original purpose as a computational tool for correspondence theory.<br />
<br />
The most important technical tools in unified correspondence are: (a) a very general syntactic definition of the class of Sahlqvist formulas, which applies uniformly to each logical signature and is given purely in terms of the order-theoretic properties of the algebraic interpretations of the logical connectives; (b) the algorithm ALBA, which effectively computes first-order correspondents of input term-inequalities, and is guaranteed to succeed on a wide class of inequalities (the so-called inductive inequalities) which, like the Sahlqvist class, can be defined uniformly in each mentioned signature, and which properly and significantly extends the Sahlqvist class.<br />
<br />
In this talk, these technical tools will be illustrated in the setting of normal lattice expansions [9]. Time permitting, constructive canonicity will be also discussed [7, 3], as well as the epistemic interpretation of modalities on RS-frames [5].<br />
<br />
References<br />
<br />
[1] M. Bilkova, G. Greco, A. Palmigiano, A. Tzimoulis, and N. Wijnberg. The logic of resources and capabilities. In preparation, 2016.<br />
<br />
[2] W. Conradie and A. Craig. Canonicity results for mu-calculi: an algorithmic approach. Journal of Logic and Computation, forthcoming. ArXiv preprint 1408.6367.<br />
<br />
[3] W. Conradie, A. Craig, A. Palmigiano, and Z. Zhao. Constructive canonicity for lattice- based fixed point logics. Submitted. ArXiv preprint 1603.06547.<br />
<br />
[4] W. Conradie, Y. Fomatati, A. Palmigiano, and S. Sourabh. Algorithmic correspondence for intuitionistic modal mu-calculus. Theoretical Computer Science, 564:30–62, 2015.<br />
<br />
[5] W. Conradie, S. Frittella, A. Palmigiano, M. Piazzai, A. Tzimoulis, and N. Wijnberg. Categories: How I Learned to Stop Worrying and Love Two Sorts. Submitted. ArXiv preprint 1604.00777.<br />
<br />
[6] W. Conradie, S. Ghilardi, and A. Palmigiano. Unified Correspondence. In A. Baltag and S. Smets, editors, Johan van Benthem on Logic and Information Dynamics, volume 5 of Outstanding Contributions to Logic, pages 933–975. Springer International Publishing, 2014.<br />
<br />
[7] W. Conradie and A. Palmigiano. Constructive canonicity of inductive inequalities. Submitted. ArXiv preprint 1603.08341.<br />
<br />
[8] W. Conradie and A. Palmigiano. Algorithmic correspondence and canonicity for distributive modal logic. Annals of Pure and Applied Logic, 163(3):338 – 376, 2012.<br />
<br />
[9] W. Conradie and A. Palmigiano. Algorithmic correspondence and canonicity for non- distributive logics. Journal of Logic and Computation, forthcoming. ArXiv preprint 1603.08515.<br />
<br />
[10] W. Conradie, A. Palmigiano, and S. Sourabh. Algebraic modal correspondence: Sahlqvist and beyond. Submitted.<br />
<br />
[11] W. Conradie, A. Palmigiano, S. Sourabh, and Z. Zhao. Canonicity and relativized canonicity via pseudo-correspondence: an application of ALBA. Submitted. Arxiv preprint 1511.04271.<br />
<br />
[12] W. Conradie, A. Palmigiano, and Z. Zhao. Sahlqvist via translation. Submitted. ArXiv preprint 1603.08220.<br />
<br />
[13] W. Conradie and C. Robinson. On Sahlqvist theory for hybrid logic. Journal of Logic and Computation, DOI: 10.1093/logcom/exv045.<br />
<br />
[14] S. Frittella, A. Palmigiano, and L. Santocanale. Dual characterizations for finite lattices via correspondence theory for monotone modal logic. Journal of Logic and Computation, forthcoming. ArXiv preprint 1408.1843.<br />
<br />
[15] G. Greco, M. Ma, A. Palmigiano, A. Tzimoulis, and Z. Zhao. Unified correspondence as a proof-theoretic tool. Journal of Logic and Computation, forthcoming. ArXiv preprint 1603.08204.<br />
<br />
[16] A. Palmigiano, S. Sourabh, and Z. Zhao. J ́onsson-style canonicity for ALBA-inequalities. Journal of Logic and Computation, DOI:10.1093/logcom/exv041.<br />
<br />
[17] A. Palmigiano, S. Sourabh, and Z. Zhao. Sahlqvist theory for impossible worlds. Journal of Logic and Computation, forthcoming. ArXiv preprint 1603.08202.<br />
<br />
<br />
----<br />
<br />
=== Monday, April 18th at 2:30pm (tea and cookies at 2:00pm) ===<br />
<br />
==== ''Speaker:'' '''Isabel M. Serrano (CSUF)''' ====<br />
<br />
''Title:'' '''Geometry in the Dark Ages'''<br />
<br />
''Abstract:'' Isidore's Etymologies enjoyed a wide audience during the<br />
medieval period. We examine the structure of mathematics, as it is<br />
described in the Etymologies, and we discuss the sources on which<br />
Isidore relied when he collected his etymological definitions. We<br />
remark that for Isidore, mathematics is described as ``the science of<br />
learning'', and among his sources there have been the classical Greek<br />
authors, most likely available in Boethius' and Cassiodorus' Latin<br />
translations performed in the early 6th century. These translations<br />
are today lost. That's why the authors writing in the middle ages had<br />
to start from scratch in many of their investigations. We will<br />
illustrate this idea with one example, namely the discovery of<br />
curvature. In a paper published in 1952, J. L. Coolidge points out<br />
that ``the first writer to give a hint of the definition of curvature<br />
was the fourteenth century writer Nicolas Oresme". Coolidge writes<br />
further: ``Oresme conceived the curvature of a circle as inversely<br />
proportional to the radius; how did he find this out?" Tractatus de<br />
configurationibus qualitatum et motuum, written by Orseme sometime<br />
between 1351 and 1355, contains the key.<br />
<br />
----<br />
<br />
=== Wednesday, April 13th at 4pm (tea and cookies at 3:30pm) ===<br />
<br />
==== ''Speaker:'' '''Matt Pusey (Perimeter Institute)''' ====<br />
<br />
''Title:'' '''From the Kochen-Specker theorem to robust noncontextuality inequalities'''<br />
<br />
''Abstract:'' Published in 1967, the Kochen-Specker theorem shows that quantum<br />
measurements do not simply reveal pre-existing values (satisfying a<br />
natural requirement). A different result along these lines, Bell's<br />
theorem, has had a much larger impact on quantum information. I will<br />
argue that this is because Bell's theorem has a clear operational<br />
meaning, independent of the quantum formalism and directly relevant to<br />
experiment. This is the motivation for various attempts to<br />
"operationalize" the Kochen-Specker theorem, and I will describe the<br />
approach to this I find most compelling. To the extent that this<br />
operationalization has succeeded, the audience should not require any<br />
knowledge of quantum theory to understand it!<br />
<br />
----<br />
<br />
=== Wednesday, April 13th at 11am (tea and cookies at 10:30am) ===<br />
<br />
==== ''Speaker:'' '''Luca Spada, University of Salerno, Italy''' ====<br />
<br />
''Title:'' '''A general algebraic approach to dualities'''<br />
<br />
''Abstract:'' In this talk I will show how several dualities in mathematics e.g., the ones of Gelfand, Pontryagin, Stone, etc. can be seen as the manifestation of a general framework in which one develops the algebraic geometry of structures different from fields. This is a joint work with O. Caramello (University Paris Diderot) and V. Marra (University of Milan).<br />
<br />
----<br />
<br />
=== Monday, February 15th at 4:00pm (tea and cookies at 3:30pm) ===<br />
<br />
==== ''Speaker:'' '''Mircea Pitici, Ph.D. in Mathematics Education, Cornell University''' ====<br />
<br />
''Title:'' '''Interpreting Mathematics, Counterfactuals, and the Paradox of Reward'''<br />
<br />
''Abstract:'' I will describe how he uses the vast literature on mathematics in my Writing in Mathematics seminar, how it relates to The Best Writing on Mathematics series I edit for Princeton, and how it matters to my teaching of mathematics and worldview.<br />
<br />
<br />
----<br />
<br />
=== Saturday, February 6th, 2016 in Von Neumann Hall ===<br />
<br />
==== 8th Annual CECAT Workshop in Pointfree Mathematics ====<br />
<br />
'''Hosted by the Center of Excellence in Computation, Algebra and Topology (CECAT)'''<br />
<br />
Held at Chapman University, Von Neumann Hall (545 W. Palm Ave, Orange, CA 92866)<br />
<br />
'''Program'''<br />
<br />
10.00am-10.50am '''Andrew Moshier (Chapman University)'''<br />
<br />
"Contexts that determine locales"<br />
<br />
11:00 - 11:50am '''Ales Pultr (Charles University, Prague)'''<br />
<br />
"An aspect of scatteredness in frames"<br />
<br />
12:00 - 12:50pm '''Papiya Bhattacharjee (Pennsylvania State University, Erie)'''<br />
<br />
"Complemented frames"<br />
<br />
2:00 - 2:50pm '''Peter Jipsen (Chapman University)'''<br />
<br />
"Duality for (residuated) lattices and correspondence theory"<br />
<br />
3:00 - 3:50pm '''Joanne Walters-Wayland (CECAT)'''<br />
<br />
"Smallest dense C and C*-quotients" <br />
<br />
<br />
----<br />
<br />
=== Friday, January 8th at 10:00am (tea and cookies at 9:30am) ===<br />
<br />
==== ''Speaker:'' '''Professor Paula Cerejeiras, Departamento de Matematica, Universidade de Aveiro, Portugal''' ====<br />
<br />
''Title:'' '''Applications of the monogenic signal processing to radiological images'''<br />
<br />
''Abstract:'' Medical ultrasonography imaging for nodule detection is a<br />
non-invasive diagnostic test, which combines low cost, short<br />
acquisition time, and sensitivity to the number and size of abnormal<br />
nodules. However, a chief problem is that ultrasound images have low<br />
contrast, making it hard for the experts to interpret and classify the<br />
nodules detected. In this talk we discuss techniques based on the<br />
concepts of monogenic signal which aims to enhance the edges of<br />
abnormalities. Hereby, we use a combination of Riesz transforms and<br />
monogenic curvelets in order to determine the phase and phase angle of<br />
a given image. Riesz transforms have remarkable properties: they are<br />
shift- and scale-invariant, preserve $L^2$ inner-product, and are<br />
steerable. Based on this approach, one is able to determine size and<br />
position of abnormalities present in images.<br />
<br />
----<br />
<br />
=== Thursday, January 7th at 4pm (tea and cookies at 3:30pm) ===<br />
<br />
==== ''Speaker:'' '''Professor Uwe Kahler, Departamento de Matematica, Universidade de Aveiro, Portugal''' ====<br />
<br />
''Title:'' '''Compressed sensing for quaternionic representation of color images'''<br />
<br />
''Abstract:'' In the last decade a new paradigm has taken hold in<br />
signal and image processing: compressed sensing. The possibility of<br />
reconstructing a signal by only a few measurements under the condition<br />
that the representation in a given basis or frame is sparse has<br />
allowed to look at new methods and algorithms. Although sparsity<br />
constraints are directly connected only with non-convex optimization<br />
the uniqueness property shown by Candes, Rhomberg, and Tao allows the<br />
application of simple convex algorithms, such as linear<br />
programming. In parallel, during the last 15 years quaternion-valued<br />
functions have been used to represent color images, in particular RGB<br />
images. Hereby, representations using the discrete and continuous<br />
quaternionic Fourier transforms play a particular important role. In<br />
this talk we will show that it is possible to combine both approaches,<br />
i.e. to use sparse sampling methods in the quaternionic representation<br />
of color images. This is a priori not so evident due to the<br />
non-commutative structure of the quaternions. For instance, it is not<br />
clear that quaternionic sampling matrices will fulfil the RIP<br />
condition as the traditional condition for compressed<br />
sensing. Therefore, we intend to go back to the origins of compressed<br />
sensing and follow the original approach by Rauhut to show that<br />
quaternionic color images allow sparse reconstruction by means of an<br />
$l_1$-minimization with high probability.</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=MathCS_Seminar_2017&diff=7MathCS Seminar 20172021-02-22T18:30:37Z<p>Jipsen: Created page with " == Fall 2017 == The seminar talks are in Von Neumann Hall VN 116 (545 W Palm Ave corner of W Palm Ave and railroad, Orange, CA 92866). Sometimes there will be a change of ve..."</p>
<hr />
<div><br />
== Fall 2017 ==<br />
<br />
The seminar talks are in Von Neumann Hall VN 116 (545 W Palm Ave<br />
corner of W Palm Ave and railroad, Orange, CA 92866).<br />
Sometimes there will be a change of venue and the announcement will reflect this change.<br />
<br />
See [http://www.chapman.edu/discover/maps-directions/index.aspx Maps<br />
and directions], Von Neumann Hall is Building 48 on the Campus Map [https://www.chapman.edu/about/_files/maps-and-directions/current-maps/campus-map.pdf <br />
Campus map]<br />
<br />
<br />
<br />
<br />
----<br />
<br />
=== Friday, December 15th at 4:00pm (Argyros Forum 212) ===<br />
<br />
==== ''Speaker:'' ''' Dr. Andrew Jordan from University of Rochester, and Kater Murch from Washington University in St. Louis ''' ====<br />
<br />
''Title:'' ''' The arrow of time in quantum mechanics'''<br />
<br />
''Abstract: '' The question of why we perceive time moving from past to future is perplexing, especially in light of the fact that microscopic laws of motion are the same running forward or backwards in time. Some have thought that the answer to this puzzle may lay in quantum wavefunction collapse. We will discuss how recent experiments have shown that quantum measurement may not be as irreversible as commonly thought, and discuss deep questions relating to the flow of time and quantum physics. We will approach the topic from three points of view, that of the experimentalist, the quantum theorist, and the philosopher.<br />
<br />
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----<br />
<br />
=== Thursday, December 14th at 4:00pm (Argyros Forum 212) ===<br />
<br />
==== ''Speaker:'' ''' Dr. Kater Murch from Washington University in St. Louis ''' ====<br />
<br />
''Title:'' ''' Measurement and control in superconducting qubits: from the quantum Zeno effect to quantum enhanced metrology '''<br />
<br />
''Abstract: '' The quantum Zeno effect is a feature of measurement-driven quantum evolution where frequent measurement inhibits the decay of a quantum state. We will explore how the opposite effect; the anti-Zeno effect - where frequent measurement accelerates decay - can also emerge from frequent measurement. The emergence of one effect or the other elucidates the nature of quantum measurement and the role measurement plays in controlling quantum evolution. In a second experiment, we investigate how control over a single qubit can be used achieve a quantum speedup in the precision of frequency measurements, demonstrating a frequency sensitivity that improves as 1/T^2, where T is the duration of the experiment.<br />
<br />
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<br />
=== Thursday, December 14th at 1:00pm (Argyros Forum 212) ===<br />
<br />
==== ''Speaker:'' ''' Dr. Alyssa Ney from UC Davis''' ====<br />
<br />
''Title:'' ''' Physics and Fundamentality '''<br />
<br />
''Abstract: '' What justifies the allocation of funding to research in physics when many would argue research in the life and social sciences may have more immediate impact in transforming our world for the better? Many of the best justifications for such spending depend on the claim that physics enjoys a kind of special status vis-a-vis the other sciences, that physics or at least some branches of physics exhibit a form of fundamentality. The goal of this paper is to articulate a conception of fundamentality that can support such justifications. I argue that traditional conceptions of fundamentality in terms of dynamical or ontic completeness rest on mistaken assumptions about the nature and scope of physical explanations.<br />
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<br />
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<br />
=== Monday, December 11th at 3:00pm (tea and cookies at 2:30pm, in VN) ===<br />
<br />
==== ''Speaker:'' ''' Dr. Gabriel Uzquiano (USC)''' ====<br />
<br />
''Title:'' ''' Cantorian arguments and the limits of thought '''<br />
<br />
''Abstract: '' Cantor’s theorem has often been thought to play a central role in Kaplan’s paradox for possible worlds semantics for intensional logic. Though we argue that Cantorian reasoning doesn't ultimately reach at the root of the problem, we suggest that some versions of the theorem may in fact be used as a heuristic for arriving at more informative results in the vicinity of Kaplan’s observation.<br />
<br />
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<br />
<br />
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<br />
=== Friday, December 1st at 3:00pm (tea and cookies at 2:30pm, in VN) ===<br />
<br />
==== ''Speaker:'' '''Sarah Alexander and Nadiya Upegui, under the supervision of Prof. Peter Jipsen, Chapman University''' ====<br />
<br />
''Title:'' ''' Partial Algebras and their Applications in Generalizations of Effect Algebras '''<br />
<br />
''Abstract: '' A partial algebra is an algebra where at least one of its operations is partial. Like total algebras, partial algebras have their own concepts of homomorphisms, subalgebras, products, and congruences that account for partiality. An effect algebra is a partial algebra with a partial binary operation + that satisfies associativity and commutativity and induces a natural partial order with a bottom element 0 and a top element 1. It also contains a total unary operation ’, behaving in such a way that for all x there exists an x’ such that x+x’=1. Effect algebras can be generalized or specialized by adding or removing axioms to change their structure. A much more general class related to effect algebras is the class of generalized pseudo-effect algebras (GPEAs). GPEAs maintain associativity but are no longer commutative and need not have a unary operation ’ nor a single maximum element. It can be proven that the existence of the unary operation ’ in effect algebras in conjunction with some of the other axioms implies that + is cancellative and that 0 acts as an identity for +. These results cannot be deduced when working with GPEAs, so these properties are adopted in the GPEA axiomitization. This class of algebras also assumes a weaker notion of commutativity called conjugation. Taking a maximal element and adding it to or removing it from a GPEA creates another GPEA, and this result is the basis for a more efficient version of a Python program used to generate and enumerate these structures. Moreover, studying how changes can be made to the structure of these classes of algebras makes them easier to understand and work with. We describe two such processes, unitization and totalization, which produce involutive residuated partially ordered monoids as the resulting structures.<br />
----<br />
<br />
----<br />
<br />
=== Conference: Tuesday to Sunday, November 14th to November 19th in Sandhu Conference Center ===<br />
<br />
==== ''Speaker:'' '''Mathematics, Signal Processing and Linear Systems:<br />
New Problems and Directions''' ====<br />
<br />
''Title:'' '''Mathematics, Signal Processing and Linear Systems:<br />
New Problems and Directions'''<br />
<br />
''Abstract: '' For directions, schedule, and book of abstracts, see CECHA Webpage: [http://www.chapman.edu/scst/research/centers-of-excellence/cecha/index.aspx CECHA Webpage], or the Conference Webpage: [http://www1.chapman.edu/~mbvajiac/conferences/2017Conference.html Conference Webpage]<br />
<br />
----<br />
<br />
<br />
----<br />
<br />
=== CECHA Workshop: Monday to Friday, November 6th to November 10th in VN Hall ===<br />
<br />
==== ''Speaker:'' '''Professor David Walnut, GMU''' ====<br />
<br />
''Title:'' '''An Overview of Wavelet Theory,<br />
With an eye on Superoscillations'''<br />
<br />
''Abstract: '' For a schedule, see CECHA Webpage: [http://www.chapman.edu/scst/research/centers-of-excellence/cecha/index.aspx CECHA Webpage], or the Workshop Webpage: [http://www1.chapman.edu/~mbvajiac/conferences/2017Wavelet.html Wavelet Workhsop]<br />
<br />
<br />
<br />
----<br />
<br />
<br />
----<br />
<br />
=== Friday, November 3rd at 3:00pm (tea and cookies at 2:30pm, in VN) ===<br />
<br />
==== ''Speaker:'' '''Dr. Marcy Robertson, Lecturer, School of Mathematics and Statistics, University of Melbourne''' ====<br />
<br />
''Title:'' ''' TBA'''<br />
<br />
''Abstract: '' TBA<br />
<br />
Dr. Robertson's Webpage: [http://www.marcyrobertson.com Dr. Marcy Robertson]<br />
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<br />
----<br />
<br />
=== Thursday, November 2nd at 4:00pm (tea and cookies at 3:30pm, in VN) ===<br />
<br />
==== ''Speaker:'' '''Dr. Alain Yger (University of Bordeaux)''' ====<br />
<br />
''Title:'' ''' Transposing (p,q) - Calculus from the Complex to the Real setting, Applications'''<br />
<br />
''Abstract: '' I will discuss in this talk the various presentations of the so-called theory of super (p,q) currents in the real setting (initiated by A. Lagerberg), together the relations it induces between the Fourier and Legendre-Fenchel dualities. Some applications towards number theory will be also discussed. It seems also that such ideas could be explored in other settings than the complex versus real one (for example quaternionic versus complex). I will in particular speak about the work of my student Robert Gualdi about getting closed formulaes for the logarithmic arithmetic height of an algebraic hypersurface in a toric variety; I will, if time permits, present a certain number of tools that could be necessary in order to extend the codimension one result to the higher codimension case.<br />
----<br />
<br />
----<br />
<br />
=== Friday, October 27th at 3:00pm (tea and cookies at 2:30pm, in VN) ===<br />
<br />
==== ''Speaker:'' ''' Dr. Ahmed Sebbar, University of Bordeaux ''' ====<br />
<br />
''Title:'' '''Harmonic series, Harmonic sums and the Riemann Hypothesis'''<br />
<br />
''Abstract: '' The harmonic series <br />
$$1+\frac{1}{2}+ \frac{1}{3}+\frac{1}{4}+\cdots $$ is one the most known series. It diverges. <br />
We comment on why the series<br />
$ \sum \frac{1}{p} $<br />
(the sum is over all the primes) also diverges, however the sum $ \sum^{'} \frac{1}{n} $ where the sum is over all the integers whose decimal expansion has no nines converges.<br />
<br />
In the second part of the talk we comment on a beautiful result of G. Robin (Limoges University) and J. Lagarias (University of Michigan) concerning the harmonic numbers<br />
$\displaystyle H_n= 1+\frac{1}{2}+ \frac{1}{3}+\frac{1}{4}+\cdots+ \frac{1}{n} $<br />
saying that if $\displaystyle \sigma_1(n) $ is the sum of the divisors of $n$ and if<br />
$\displaystyle \sigma_1(n) \leq e^{H_n} \log H_n +H_n$<br />
then the Riemann hypothesis is true. This is a very elementary formulation of a Millennium Problem.<br />
<br />
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<br />
=== Wednesday, October 25th at 2:30pm (Argyros Forum 208) ===<br />
<br />
==== ''Speaker:'' ''' George Csicsery, Visiting Documentary Filmmaker''' ====<br />
<br />
''Title:'' ''' Finding the hook '''<br />
<br />
''Abstract: '' Filmmaker George Csicsery will discuss how he presents mathematics and mathematicians to lay audiences in a society with attention deficit disorder. Excepts from his films “N is a Number: A Portrait of Paul Erdös” (1993), “Julia Robinson and Hilbert’s Tenth Problem” (2008,” “Hard Problems” (2008), “Counting from Infinity” (2015), and “Navajo Math Circles” (2016), will be used to illustrate his main theme: that scientific ideas and math can be smuggled into a story when there is suspense, drama or genuine human interest at the foundation.<br />
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=== Saturday, October 21st at 3:00pm (tea and cookies at 2:30pm, in VN) ===<br />
<br />
==== ''Speaker:'' '''Mathematical Association of America Meeting''' ====<br />
<br />
''Title:'' ''' MAA Fall 2017 SoCal-Nevada Section Meeting '''<br />
<br />
''Abstract: '' See the MAA Webpage: [http://sections.maa.org/socalnv/ SoCal-Nevada MAA Webpage]<br />
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=== Friday, October 20th at 3:00pm (tea and cookies at 2:30pm, in VN) ===<br />
<br />
==== ''Speaker:'' ''' Guillaume Jeremie Massas (UCI)''' ====<br />
<br />
''Title:'' '''Constructive representations of Heyting algebras and semantics for Intuitionistic Predicate Logic'''<br />
<br />
''Abstract: '' Model Theory and the theory of Boolean algebras are two fruitful tools for investigating classical logic. Gödel’s completeness theorem and Stone’s representation theorem are regarded as cornerstones of each field respectively. The celebrated Rasiowa-Sikorski lemma allows one to construct term models out of ultrafilters on Boolean algebras, thus bridging the gap between the two: Rasiowa and Sikorski’s original proof relied on Stone’s representation theorem, and their lemma was used to give a purely algebraic proof of Gödel's completeness theorem. However the general methods behind this approach, because of their appeal to ultrafilters, are highly non-constructive.<br />
Over the years, various generalizations of Stone’s theorem, of Gödel’s theorem, and of the Rasiowa-Sikorski lemma have taken either of the two orthogonal directions:<br />
<br />
generalizing the results to wider classes of logics and algebras (in particular to intuitionistic logic and Heyting algebras);<br />
working under restricted forms of the axiom of choice and providing more constructive proofs.<br />
In this talk, I will present how to combine the two programs. I will first provide more constructive versions of the Rasiowa-Sikorski Lemma and constructive representation theorems for distributive lattices and Heyting algebras. I will then combine those two results to define a constructive semantics for intuitionistic predicate logic, and show how it generalizes existing semantics.<br />
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<br />
=== Friday, October 6th at 3:00pm (tea and cookies at 2:30pm, in VN) ===<br />
<br />
==== ''Speaker:'' ''' David Wallace (USC)''' ====<br />
<br />
''Title:'' '''What is orthodox quantum mechanics?'''<br />
<br />
''Abstract: '' What is called ``orthodox'' quantum mechanics, as presented in standard foundational discussions, relies on two substantive assumptions --- the projection postulate and the eigenvalue-eigenvector link --- that do not in fact play any part in practical applications of quantum mechanics. I argue for this conclusion on a number of grounds, but primarily on the grounds that the projection postulate fails correctly to account for repeated, continuous and unsharp measurements (all of which are standard in contemporary physics) and that the eigenvalue-eigenvector link implies that virtually all interesting properties are maximally indefinite pretty much always. I present an alternative way of conceptualising quantum mechanics that does a better job of representing quantum mechanics as it is actually used, and in particular that eliminates use of either the projection postulate or the eigenvalue-eigenvector link, and I reformulate the measurement problem within this new presentation of orthodoxy.<br />
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<br />
=== Friday, September 29th at 3:00pm (tea and cookies at 2:30pm, in VN) ===<br />
<br />
==== ''Speaker:'' ''' Dr. Justin Dressel, Chapman University''' ====<br />
<br />
''Title:'' ''' Watching a quantum system: How to continuously measure a superconducting qubit'''<br />
<br />
''Abstract: '' It has recently become experimentally possible to monitor the energy levels of a superconducting transmon qubit continuously in time using microwave fields. Such measurements weakly perturb the qubit per unit time, lead to a competition between unitary Hamiltonian dynamics and non-unitary collapse dynamics. I review several subtleties about modeling this measurement process, and discuss several recent achievements made in collaboration with the Siddiqi laboratory at UC Berkeley. Topics include simultaneous measurements of multiple non-commuting observables, the active use of the quantum Zeno effect with a moving measurement basis for qubit control, and subtle aspects about the information content contained in the collected stochastic readout.<br />
<br />
Bio: <br />
Justin Dressel received his Ph.D. in quantum physics from U Rochester in 2013, was a visiting researcher at RIKEN Wako-shi in Saitama, Japan in 2013, and was a postdoctoral scholar at UC Riverside between 2013-2015, after which he started as an Assistant Professor in Physics and Computational Science at Chapman University. He researches quantum information, computing, and foundations, which is a natural intersection point between physics, mathematics, and computer science. His recent research has focused on algebraic approaches to generalized quantum measurements, quantum computation with superconducting transmon quantum bits using circuit quantum electrodynamics, and Clifford algebraic approaches to relativistic field theory. Though the bulk of his work is theoretical in nature, he works closely with experimental teams whenever possible.<br />
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=== Friday, September 22nd at 2:00pm (tea and cookies at 1:30pm, in VN) ===<br />
<br />
==== ''Speaker:'' '''Dr. Ahmed Sebbar, University of Bordeaux''' ====<br />
<br />
''Title:'' '''Algebraic methods in analytic questions Second Example'''<br />
<br />
''Abstract: ''The talk concerns some arithmetic and algebraic questions behind the paperfolding. One of its main objectives is to study the power series<br />
\begin{equation}\label{new} \xi(z)= \sum_{n\geq 1} s_n z^n,\; \; |z|<1 <br />
\end{equation}<br />
where $(s_n)$ is the paperfolding sequence defined by<br />
\[s_{2n}= s_n,\quad s_{2n+1}= (-1)^n, \quad n\in \mathbb{Z}_+ .\]<br />
<br />
This sequence arises as follows: A sheet of paper can be folded once right half over left or left half over right. During the talk we explore the dynamics of a continued fraction related to $ \xi(z) $, and also a relation of the problem with the modularity theorem(formerly the Taniyama-Shimura-Weil conjecture). <br />
<br />
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<br />
=== Thursday, September 14th at 4:15pm (tea and cookies at 3:45pm, in VN) ===<br />
<br />
==== ''Speaker:'' '''Dr. Ahmed Sebbar, University of Bordeaux''' ====<br />
<br />
''Title:'' '''Algebraic methods in analytic questions First Example'''<br />
<br />
''Abstract: '' For a fixed $x$, we consider the two functions in $h$, analytic near the origin:<br />
\[\phi(h)= \log\left(1+3hx-h^3\right)†= \sum_{n=0}^{\infty} P_n(x) h^n†\]<br />
and<br />
\[\psi(h)= \log\left(1+3h^2x-h^3\right)†= \sum_{n=0}^{\infty} Q_n(x) h^n†\]<br />
with polynomials in $x$, $P_n(x)$ and $Q_n(x)$. We wonder whether there is a relationship between $P_n(x)$ and $Q_n(x)$. The positive answer to this question depends on the peculiarities of the two quadratic extensions $\mathbb{Q}(i) $ and $\mathbb{Q}(\rho), \rho= \frac{-1+i\sqrt{3}}{2} $ and their relation with theory of complex multiplication for elliptic curves (Lemniscatomic and anharmonic cases). We give a brief history of Class Field Theory, Clausen hypergeometric function and the answer to the question. We show that the polynomials $P_n(x)$ and $Q_n(x)$ have some divisibillity propriety, similar to the one for Lucas sequences.<br />
<br />
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<br />
=== Thursday, September 7th at 4:15pm (tea and cookies at 3:45pm, in VN) ===<br />
<br />
==== ''Speaker:'' '''Dr. Imanol Mozo Carollo, Chapman University''' ====<br />
<br />
''Title:'' '''On subspaces of pointfree bitopological spaces and their smallest dense subspace'''<br />
<br />
''Abstract: '' With the purpose of finding a Stone duality for bitopological spaces, A. Jung and A. Moshier introduced in the category of d-frames in which objects are structures that comprise two frames, thought of as lattices of open sets, and two relations that connect both frames, as abstractions of the covering and disjointness relation. The aim of this talk is to explore an approach to the notion of parts of a space in this pointfree bitopological setting.<br />
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=== Friday, September 1st at 5:00pm (tea and cookies at 4:30pm, in VN) ===<br />
<br />
<br />
==== ''Speaker:'' '''Dr. Razieh Mohseninia, Sharif University of Technology''' ====<br />
<br />
''Title:'' '''Topological quantum computation and the stability of topological memories'''<br />
<br />
''Abstract: '' Quantum computers are necessary to simulate quantum systems. The fragility of qubits in presence of decoherence and external noise is the biggest obstacle in realizing a quantum computer. To overcome such problems, topological quantum computation has been introduced by Kitaev that combines the main quantum feature of the quantum world, namely, superposition of states, with the robustness of classical bits which is the result of a macroscopic number of very small entities, comprising each bit. In this way, topological features which are robust against local perturbations are used for storing information. It is well-known that the $Z_3$ Kitaev model can be used to perform universal quantum computation. Due to unwanted interactions in the system, perturbations may be added to a possible realization of the system. In the first part of my talk, stability of the $Z_3$ Kitaev model in the presence of external perturbations in the form of Potts interaction is studied. Our study relies on two high-order series expansions based on continuous unitary transformations in the limits of small and large Potts couplings as well as mean-field approximation. Our analysis reveals that the topological phase of the $Z_3$ Kitaev model breaks down to the Potts model through a first-order phase transition. Another example of topological memories is the Topological Color Code, which in 2 dimensions can be used for implementing the Clifford group in a fully topological and transversal manner. In the second part of my talk, I study thermal stability of this model in presence of a thermal bath. The auto-correlation functions of the observables are used as a figure of merit for the thermal stability. I show that all of the observables auto-correlation functions decay exponentially in time. By finding a lower bound on the decay rate, which is a constant independent of the system size, I show that the Topological Color Code is unstable against thermal fluctuations from the bath at finite temperature, even though it is stable at $T=0$ against local quantum perturbations.<br />
<br />
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<br />
== Summer 2017 ==<br />
<br />
The seminar talks are in Von Neumann Hall VN 116 (545 W Palm Ave<br />
corner of W Palm Ave and railroad, Orange, CA 92866).<br />
Sometimes there will be a change of venue and the announcement will reflect this change.<br />
<br />
See [http://www.chapman.edu/discover/maps-directions/index.aspx Maps<br />
and directions], Von Neumann Hall is Building 38 on the<br />
[http://www.chapman.edu/discover/_files/CU_CampusMap2012-13-2.pdf<br />
Campus map]<br />
<br />
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<br />
=== Wednesday, July 26th at 4:00pm (tea and cookies at 3:30pm, in VN) ===<br />
<br />
==== ''Speaker:'' '''Dr. Angelyn R. Lao, Department of Mathematics, De La Salle University, Philippines''' ====<br />
<br />
''Title:'' '''Systems Approaches in Making Sense of Data and Providing Meaning to Biological Models'''<br />
<br />
''Abstract: '' Systems biology is an interdisciplinary approach that aims at understanding the dynamic interactions between components of biological system. It is also an approach by which biological questions are addressed through integrating experiments in iterative cycles with computational modelling, simulation and theory. This approach is best applied when there is synergistic usage of the models and data. As such that the models established are meaningful and make sense to the collected data. Depending on the types, quality, and amount of data and the purpose of the model, the kind of modeling approaches will also vary. Modelling is not the final goal, but is a tool to increase understanding of the system, to develop more directed experiments and finally allow predictions.<br />
Why model? By modeling, we aim to guide data collection, discover new questions, formulate hypotheses, and reveal simplicity in complexity. There are different ways of modeling. One of the most popular approaches is the use of ordinary differential equations (ODE) to model the interactome among the components of a system. Other modeling approaches include stochastic modeling, Boolean modeling, agent-based modeling and etc.<br />
Systems biology is a cross talk between different disciplines. It requires interdisciplinary collaboration between fields like biology, physics, computer science and engineering, with the goal of having a deeper insight of the functional bases of life. <br />
<br />
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<br />
== Spring 2017 ==<br />
<br />
The seminar talks are in Von Neumann Hall VN 116 (545 W Palm Ave<br />
corner of W Palm Ave and railroad, Orange, CA 92866).<br />
Sometimes there will be a change of venue and the announcement will reflect this change.<br />
<br />
See [http://www.chapman.edu/discover/maps-directions/index.aspx Maps<br />
and directions], Von Neumann Hall is Building 38 on the<br />
[http://www.chapman.edu/discover/_files/CU_CampusMap2012-13-2.pdf<br />
Campus map]<br />
<br />
<!--'''Note:''' This semester we will (for now) start talks '''at 1:15<br />
pm'''. From 12:45 pm to 1:15 pm is time for refreshments and<br />
interesting conversations with the speaker, so consider coming a bit<br />
early.--><br />
<!--<br />
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== Upcoming Talks and Workshops ==<br />
--><br />
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=== Friday, May 26th at 2:00pm (tea and cookies at 1:30pm, in AF 212) ===<br />
<br />
==== ''Speaker:'' '''Dr. Eleanor Rieffel, Quantum Artificial Intelligence Laboratory, NASA Ames Research Center''' ====<br />
<br />
''Title:'' '''A NASA Perspective on Quantum Computing: Opportunities and Challenges'''<br />
<br />
''Abstract: '' The success of the abstract model of computation, in terms of bits, logical operations, algorithms, and programming language constructs makes it easy to forget that computation is a physical process. Our cherished notions of computation and information are grounded in classical mechanics, but the physics of our universe is quantum. A natural question to ask is how computation would change if we adopted a quantum mechanical, instead of a classical mechanical, model of computation.<br />
In the early 80s, Richard Feynman, Yuri Manin, and others recognized that certain quantum effect could not be simulated efficiently on conventional computers. This observation led researchers to speculate that perhaps such quantum effect could be used to speed up computation more generally. Slowly, a new picture of computation arose, one that gave rise to a variety of faster algorithms, novel cryptographic mechanisms, and alternative methods of communication. <br />
<br />
For most computational problems, however, it is currently unknown whether quantum algorithms can provide an advantage, and if so by how much, or how to design quantum algorithms that realize such advantages. Many of the most challenging computational problems arising in the practical world are tackled today by heuristic algorithms that have not been mathematically proven to outperform other approaches but have been shown to be effective empirically. While quantum heuristic algorithms have been proposed, empirical testing becomes possible only as quantum computation hardware is built. The next decade promises to be exciting emerging hardware makes empirical testing of quantum heuristic algorithms more and more feasible.<br />
<br />
In the first part of the talk, I will introduce key concepts underlying quantum computing and correct common misconceptions. In the second half of the talk, I will discuss applications of quantum computing, known advantages and limitations, including work at NASA on quantum heuristics. I will briefly touch on the current state-of-the-art in building quantum computers, quantum error correction and fault tolerance, and the many open research questions that remain. <br />
<br />
<br />
Bio: Eleanor G. Rieffel leads the Quantum Artificial Intelligence Laboratory<br />
at the NASA Ames Research Center. She joined NASA Ames Research Center in 2012 to work on their expanding quantum computing effort, after working at FXPAL where she performed research in diverse fields including quantum computation, applied cryptography, image-based geometric reconstruction of 3D scenes, bioinformatics, video surveillance, and automated control code generation for modular robotics.<br />
Her research interests include quantum heuristics, evaluation and utilization of near-term quantum hardware, fundamental resources for quantum computation, quantum error suppression, and applications for quantum computing. She received her Ph.D. in mathematics from the University of California, Los Angeles. She is best known for her 2011 book Quantum Computing: A Gentle Introduction with coauthor Wolfgang Polak and published by MIT press.<br />
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<br />
=== Friday, May 19th at 2:00pm (tea and cookies at 1:30pm) ===<br />
<br />
==== ''Speaker:'' '''Prof. Miguel Navascues, IQOQI Vienna''' ====<br />
<br />
''Title:'' '''Random variables, entanglement and nonlocality in infinite translation-invariant systems'''<br />
<br />
''Abstract: '' We consider the problem of certifying entanglement and nonlocality in one-dimensional translation-invariant (TI) infinite systems when just averaged near-neighbor correlators are available. Exploiting the triviality of the marginal problem for 1D TI distributions, we arrive at a practical characterization of the near-neighbor density matrices of multi-separable TI quantum states. This allows us, e.g., to identify a family of separable two-qubit states which only admit entangled TI extensions. For nonlocality detection, we show that, when viewed as a vector in R^n, the set of boxes admitting an infinite TI classical extension forms a polytope, i.e., a convex set defined by a finite number of linear inequalities. Using DMRG, we prove that some of these inequalities can be violated by distant parties conducting identical measurements on an infinite TI quantum state. Both our entanglement witnesses and our Bell inequalities can be used to certifyentanglement and nonlocality in large spin chains (namely, finite, and not TI chains) via neutron scattering. <br />
<br />
Our attempts at generalizing our results to TI systems in 2D and 3D lead us to the virtually unexplored problem of characterizing the marginal distributions of infinite TI systems in higher dimensions. In this regard, we show that, for random variables which can only take a small number of possible values (namely, bits and trits), the set of nearest (and next-to-nearest) neighbor distributions admitting a 2D TI infinite extension forms a polytope. This allows us to compute exactly the ground state energy per site of any classical nearest-neighbor Ising-type TI Hamiltonian in the infinite square or triangular lattice. Remarkably, some of these results also hold in 3D. In contrast, when the cardinality of the set of possible values grows (but remaining finite), we show that the marginal nearest-neighbor distributions of 2D TI systems are not described by a polytope or even a semi-algebraic set. Moreover, the problem of computing the exact ground state energy per site of arbitrary 2D TI Hamiltonians is undecidable.<br />
<br />
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=== Wednesday, May 17th at 2:30pm (tea and cookies at 2:00pm) ===<br />
<br />
==== ''Speaker:'' '''Prof. Daniel Alpay, Chapman University''' ====<br />
<br />
''Title:'' '''Non-commutative Brownian Motion and a New Class of Topological Algebras'''<br />
<br />
''Abstract: '' We study a family of free stochastic processes whose covariance kernels K may be derived as a transform of a tempered measure σ. These processes arise, for example, in consideration non-commutative analysis involving free probability. Hence our use of semi-circle distributions, as opposed to Gaussians. In this setting we find an orthonormal bases in the corresponding non-commutative L2 of sample-space. We define a stochastic integral for our family of free processes. <br />
<br />
Joint work with Palle Jorgensen and Guy Salomon<br />
<br />
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=== Friday, May 12th at 2:00pm (tea and cookies at 1:30pm) ===<br />
<br />
==== ''Speaker:'' '''Prof. Abhijit Banerjee, Krishnath College, Berhampore, Calcutta''' ====<br />
<br />
''Title:'' '''Mathematical Formulations of PT Symmetric Bicomplex Quantum Mechanics'''<br />
<br />
''Abstract: '' With a view to obtaining further insight into the nature of eigenvalues and eigenfunctions of a stationary state one-dimensional Schrodinger equation corresponding to a PT-symmetric bicomplex Hamiltonian H we present the mathematical formulations of an analogous version of the Schrodinger equation. Since in such a setting three different types of conjugates of bicomplex numbers appear, each is found to define, in a natural way, a separate class of time reversal operator. However, the induced parity (P)-time (T)-symmetric models turn out to be mutually incompatible, except for two of them which could be chosen uniquely. The later models are then explored by working within an extended phase space. Applications to the problems of harmonic oscillator and isotonic oscillator are considered and many new interesting properties are uncovered for the new types of PT symmetries.<br />
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<br />
=== Wednesday, May 10th at 1:00pm (tea and cookies at 2:00pm, after the seminar) ===<br />
<br />
==== ''Speaker:'' '''Dr. Purbita Jana, Department of Pure Mathematics, University of Calcutta, India ''' ====<br />
<br />
''Title:'' '''Graded Frame and related Mathematical structures'''<br />
<br />
''Abstract: '' In this talk the main focus will be the notion of graded frame and its connection with graded fuzzy topological system, fuzzy topological<br />
space with graded inclusion and fuzzy geometric logic with graded consequence. As a ground work we will first discuss the topic of Topology<br />
via Logic" written by S. Vickers, where the notion of topological system and its usefulness in duality theory as well as study of topological<br />
space via logic is mentioned. Generalizing Vickers's work step by step we will reach to the concept of graded frame, related structures and<br />
their utilities.<br />
<br />
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<br />
=== Friday, May 5th at 2:00pm (tea and cookies at 1:30pm) in collaboration with the Philosophy Department===<br />
<br />
==== ''Speaker:'' '''Prof. Alberto Naibo, Sorbonne''' ====<br />
<br />
''Title:'' '''Harmony, Stability, and Identity: An intensional account in proof-theoretic semantics'''<br />
<br />
''Abstract: '' Proof-theoretic semantics are usually conceived in opposition to truth-theoretic semantics. In truth-theoretic semantics, truth is considered as a primitive (non-analyzed) notion, and meaning is then explained in terms of it. On the other hand, in proof-theoretic semantics, meaning is explained in terms of (our) inferential abilities, and truth is then explained in terms of proofs. In order to avoid any possible trivialization of proof-theoretic semantics — boiling it down to truth-theoretic semantics — an intensional, rather than an extensional approach, should be adopted. In particular, the semantic value of a sentence A should not be defined in terms of the simple existence of a proof of A, but in terms of the way in which A is proved, i.e. in terms of the inferential structure of proof of A. In order to specify this structure some properties are asked to be satisfied. The most known of them is the property of harmony, which corresponds to the reduction of local complexity peaks (detours) in a proof. However, as Dummett claims, this property is “an excessively modest demand”, and it should be complemented by another property, that of stability. It will be shown that this property can be captured by a more fundamental operation, that of expansion, allowing one to generate local complexity riffs within a proof. Even if this operation could seem very natural to add, it will be shown in fact how it is destructive for the intensional account proper to proof-theoretic semantics. In particular, when this operation of expansion is used in presence of negation and identity, it leads to the collapse of the set of proofs of negative and identity sentences, respectively. Finally, the case of identity is analyzed in details in the framework of Martin-Löf’s type theory. It is shown, in particular, that a possible way of avoiding the collapse between identity proofs can be found in the works of M. Hoffman and T. Streicher, where the operation of expansion is lifted from the level of proof-objects to the level of the sentences which speak about these proof-objects.<br />
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<br />
=== Friday, May 5th at 12:00pm (tea and cookies at 1:30pm) in collaboration with the Philosophy Department===<br />
<br />
==== ''Speaker:'' '''Professor Pierre Wagner, Sorbonne''' ====<br />
<br />
''Title:'' '''The normative character of logic and pluralism'''<br />
<br />
''Abstract: '' Logic is traditionally regarded as normative and the justification of such a view has often been that the laws of logic do not have any descriptive content: they do not describe how we do think but provide prescriptions about how we ought to think. This presupposes that logic is about thought or at least that it has something to do with reasoning. A philosophical contemporary debate about the normativity of logic questions the exact nature of the connection between logic and thought, and tries to assess the reasons for regarding logic as having a normative character. In this talk, we shall discuss this point and its essential connection with pluralism in logic.<br />
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=== Friday, April 21st at 2:00pm (tea and cookies at 1:30pm) ===<br />
<br />
==== ''Speaker:'' '''Professor H. Turgay Kaptanoglu, Department of Mathematics, Bilkent University, Ankara''' ====<br />
<br />
''Title:'' '''Precise Inclusion Relations Among Bergman-Besov and Bloch-Lipschitz Spaces and H^\infty on the Unit Ball of C^n'''<br />
<br />
''Abstract: '' We describe exactly and fully which of the spaces of holomorphic functions in the title are included in which others. We provide either new results or new proofs. More importantly, we construct explicit functions in each space that show our relations are strict and best possible.<br />
<br />
Joint work with A. Ersin Ureyen of Anadolu University, Eskisehir, Turkey<br />
<br />
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=== Tuesday, April 11th at 1:00pm (tea and cookies at 12:30pm), please note the change in date/time ===<br />
<br />
==== ''Speaker:'' '''Professor David Shoikhet, Holon Institute of Technology, The Technion Institute of Technology of Israel''' ====<br />
<br />
''Title:'' '''Old and New in Complex Dynamical Systems'''<br />
<br />
''Abstract: '' Historically, complex dynamics and geometrical function theory have been intensively developed from the beginning of the twentieth century. They provide the foundations for broad areas of mathematics. In the last fifty years the theory of holomorphic mappings on complex spaces has been studied by many mathematicians with many applications to nonlinear analysis, functional analysis, differential equations, classical and quantum mechanics. The laws of dynamics are usually presented as equations of motion which are written in the abstract form of a dynamical system: ((dx)/(dt))+f(x)=0, where x is a variable describing the state of the system under study, and f is a vector-function of x. The study of such systems when f is a monotone or an accretive (generally nonlinear) operator on the underlying space has recently been the subject of much research by analysts working on quite a variety of interesting topics, including boundary value problems, integral equations and evolution problems.<br />
In this talk we give a brief description of the classical statements which combine the celebrated Julia Theorem of 1920, Carathéodory's contribution in 1929 and Wolff's boundary version of the Schwarz Lemma of 1926 with their modern interpretations for discrete and continuous semigroups of hyperbolically non-expansive mappings in Hilbert spaces. We also present flow-invariance conditions for holomorphic and hyperbolically monotone mappings.<br />
Finally, we study the asymptotic behavior of one-parameter continuous semigroups (flows) of holomorphic mappings. We present angular characteristics of the flows trajectories at their Denjoy-Wolff points, as well as at their regular repelling points (whenever they exist). This enables us by using linearization models in the spirit of functional Schroeder's and Abel's equations and eigen-value problems for composition operators to establish new rigidity properties of holomorphic generators which cover the famous Burns-Krantz Theorem and to solve a Nevanlinna-Pick type boundary interpolation problem for generators.<br />
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=== Friday, April 7th at 2:00pm (tea and cookies at 1:30pm) ===<br />
<br />
==== ''Speaker:'' '''Dr. Imanol Mozo, Chapman University''' ====<br />
<br />
''Title:'' '''The unit circle in pointfree topology'''<br />
<br />
''Abstract: '' Pointfree topology is an lattice-theoretic approach to topology that takes abstract lattices of open sets as the primitive notion. This approach is motivated by the fact that the lattice of open sets of a topological space contain almost all the information. Indeed, some lattices, namely, frames, are sufficiently similar to lattices of open sets of topological spaces in order to be considered as generalized spaces [5].<br />
One of the main differences between pointfree topology and classical topology is that the category of frames is algebraic, while the dual of the category of topological spaces is not. Consequently, we can present its objects by generators and relations, as in an algebraic fashion. This is a very useful tool that was used by Joyal in order to introduce the pointfree counterpart of the real line [3], which was later studied by Banaschewski in [1]. Besides, this procedure offers a natural way to introduce variants by modifying the set of generators or the defining relations. For instance, one has the frame of extended reals and the lattice of extended real functions studied in [2], and the frame of partial reals and the lattice of continuous partial real functions introduced in [4] which arose naturally in the construction of the Dedekind completion of the lattice of continuous real functions on a frame.<br />
In this talk, after a brief introduction to pointfree topology, we will discuss how the topology of the unit circle fits in this family of frames.<br />
<br />
[1] B. Banaschewski, The real numbers in pointfree topology, Textos de Matemática vol. 12, Departamento de Matemática da Universidade de Coimbra (1997).<br />
[2] B. Banaschewski, J. Gutiérrez García, J. Picado, Extended real functions in pointfree topology, J. Pure Appl. Algebra 216 (2012), 905–922.<br />
[3] A. Joyal, Nouveaux fondaments de l’analyse. Lectures Montréal 1973 and 1974 (unpublished).971), 161–167.<br />
[4] I. Mozo Carollo, J. Gutiérrez García and J. Picado, On the Dedekind completion of function rings, Forum Math. 27 (2015), 2551 -2585.<br />
[5] J. Picado and A. Pultr, Frames and locales: Topology without points, Frontiers in Mathematics, vol. 28, Springer, Basel (2012).<br />
<br />
<br />
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<br />
=== Friday, March 31st at 2:00pm (tea and cookies at 1:30pm) join with the Philosophy Department===<br />
<br />
==== ''Speaker:'' '''Professor John Mumma, CalState San Bernardino''' ====<br />
<br />
''Title:'' '''Lewis's infinite regress, mathematical proof, and the act of diagramming '''<br />
<br />
''Abstract: '' In 'What the Tortoise Said to Achilles.' Carroll shows how an infinite regress can be generated from the demand that all premises in a deductive inference be made explicit. In my talk I discuss the connection of the regress to the question of how mathematical proofs are accepted as proofs. A mathematical proof does not succeed unless it can be seen how acceptance of its premises force acceptance of its conclusion. Carroll's piece can be understood, I argue, as illuminating the difficulties in providing a satisfactory account of this seeing. I then focus on a restricted class of elementary geometric inferences, and explore whether the act of diagramming them resolves (for this restricted class) the general difficulties Carroll's piece raises. <br />
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<br />
=== Friday, March 24th at 2:00pm (tea and cookies at 1:30pm) ===<br />
<br />
==== ''Speaker:'' '''Professor Dan Volok, Kansas State University, Department of Mathematics''' ====<br />
<br />
''Title:'' '''Non-stationary point evaluation in the multiscale setting'''<br />
<br />
''Abstract: '' It was demonstrated by D. Alpay, P. Dewilde and H. Dym that the Hilbert space of triangular Hilbert-Schmidt operators can be equipped with a reproducing kernel structure quite similar to that of the classical Hardy space of the unit disk. This fact has many applications in the theory of non-stationary dissipative systems. It turns out that a multivariate generalization of Alpay-Dewilde-Dym reproducing kernel Hilbert space arises naturally in the setting of linear systems indexed by homogeneous trees, as introduced by A. Benveniste, R. Nikoukhah and A. Willsky. <br />
<br />
This talk is based on joint work with D. Alpay and A. Dijksma.<br />
<br />
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<br />
=== Friday, March 17th at 2:00pm (tea and cookies at 1:30pm) ===<br />
<br />
==== ''Speaker:'' '''Professor Palle Jorgensen, University of Iowa, Department of Mathematics''' ====<br />
<br />
''Title:'' '''Markov processes, endomorphisms, and measurable dynamics'''<br />
<br />
''Abstract: '' The structures of positive operators, endomorphisms, transfer operators, measurable partitions, and Markov processes arise in both pure and applied mathematics. The talk offers unified setting, as well as new applications. The general setting is that of dynamics in Borel measure spaces and Markov fields. Hence the corresponding linear structures to be studied are infinite-dimensional. Nonetheless, we prove a number of analogues of the more familiar finite-dimensional settings, for example, the Perron-Frobenius theorem in the case of positive matrices, and the corresponding Markov chains.<br />
<br />
<br />
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<br />
=== Friday, March 10th at 2:00pm (tea and cookies at 1:30pm) ===<br />
<br />
==== ''Speaker:'' '''Professor Howard Wiseman, Griffith University, and the Centre for Quantum Computation and Communication Technology''' ====<br />
<br />
''Title:'' '''What is Quantum Markovianity?'''<br />
<br />
''Abstract: '' Markovianity versus non-Markovianity is a well-established distinction for classical systems. The same cannot be said for quantum systems. Different communities and individuals use “quantum Markovianity” to mean very different things. We argue that, to avoid confusion, it is best to avoid attributing that term any definite meaning at this stage. However, that does not mean that there is nothing to say about Markovianity for open quantum systens. We discuss a large number of concepts that have been, or could logically be, used to define quantum (non-)Markovianity, and prove hierarchical relations between them. Some are existing concepts, including “factorisation”, “quantum regression formula”, “divisibility”, and “Lindblad”. Others we introduce, including “past-future independence”, and “composability”. We also prove relations between these and other properties of interest for open quantum systems, such as the applicability of dynamical decoupling to preserve quantum information, the existence of (quantum) information backflow from the environment, and the physical reality of stochastic pure-state trajectories. Finally, we discuss in which concept the closest analogue of classical Markovianity lies.<br />
<br />
Joint work with: Li (Kenny) Li, and Michael Hall<br />
<br />
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<br />
=== Tuesday, March 7th at 5:30pm (tea and cookies at 5:00pm) ===<br />
<br />
==== ''Speaker:'' '''Professor Giuseppe Longo, CNRS, CREA, École Polytechnique, et CIRPHLES, ENS, Paris''' ====<br />
<br />
''Title:'' '''The Structuralist Roots of Mathematical Understanding Reconsidered: Poincaré’s heritage'''<br />
<br />
''Abstract: '' The theological origin of the physicomathematical spaces; the geometrization of time<br />
Abstract: There is no mathematical plane nor space in Euclid's geometry. Lines are traced, extended, intersected on a plane, an “apeiron” (it has no boundary), which is “practiced” but not mathematized. These lines have no thickness, they intersect in a point, that is a sign (“semeion”); they are objects of a mythical, ideal realm. Infinity is only potential: lines in the plane or endless sequences of numbers can be extended with no limit. Actual infinity will be fully conceptualized much later, in the theological debate of late middle age, as an attribute of God. How actual infinity relates to or how can it be represented in the finite? The Renaissance Italian painters will show that this is possible: the projective limit of the newly invented linear perspective, first used in XIV century paintings of the Annonciation, shows the infinite in the finite and joins the infinity of God to the bodily, three dimensional presence of a human being, the Madonna. We will critically analyze paintings from Giotto to Piero della Francesca that show this joint invention of actual infinity and of mathematical spaces, which allows as well the expression of a new, corporeal humanity. Later, this theological invention will become the mathematics of Descartes' and Desargues' spaces, the science of Newton's infinities. In the XIX century, physics will extend this mystical creation of infinite space and time to the mathematical “phase space” of its new scientific rigor, based on an increasing mathematical unity of space and time.<br />
<br />
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<br />
=== Friday, February 17th at 2pm (tea and cookies at 1:30pm) ===<br />
<br />
==== ''Speaker:'' '''Andrew Jordan, University of Rochester''' ====<br />
<br />
''Title:'' '''Postselection, Superconductors, and Quantum Information in Black Holes'''<br />
<br />
''Abstract: '' This talk will demonstrate how the quantum information entering black holes is analogous to quantum information entering a superconductor. The correspondence maps the interior of a black hole to a superconductor, and the exterior of the black hole to a normal metal. We show that the metal-superconductor interface can be thought of as an event horizon: The proximity effect in superconductor-metal interfaces (where Cooper pairs tend to form in the normal metal) is analogous to electron-positron creation at the event horizon in black-holes, which gives rise to Hawking radiation. Existing popular ideas of preserving quantum information entering black holes – the Preskill informational mirror, and the Horowitz-Maldacena mechanism for black-hole evaporation (which necessitates a unique final state for the black-hole), can be exactly incarnated as quantum information swapping or transfer using Andreev reflection processes. I will present mesoscopic physics analogs to wormholes and time loops using postselection on the superconducting ground state of a condensed gas of Cooper pairs – and conjecture that the BCS ground state also describes the final quantum state of a black hole.<br />
<br />
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<br />
=== Wednesday, February 15th at noon (tea and cookies at 11:30am) ===<br />
<br />
==== ''Speaker:'' '''Gerhard Heinzmann, Université de Lorraine/CNRS & Archives Henri-Poincaré (UMR 7117), Nancy, France''' ====<br />
<br />
''Title:'' '''The Structuralist Roots of Mathematical Understanding Reconsidered: Poincaré’s heritage'''<br />
<br />
''Abstract: '' This paper proposes a reconsideration of mathematical structuralism. It adopts the "practical turn" that owes much to Henri Poincare. By reconsstructing his group theoretic approach of geometry, it seems possible to explain the main difficulty of modern structuralism, inaugurated by the French collective Bourbaki around the middle of the XXth century: the unclear ontological status of ‘structures’ and ‘places’. <br />
For Poincaré, the formation of the group concept - a 'universal' - is suggested by a specific system of stipulated sensations and, read as a relational set, the general group concept constitutes a model of the group axioms, which are exemplified (in the Goodmanien sense) by the sensation system. In other words, the shape created in the mind leads to a particular type of platonistic universals, which is a model (in the model theoretical sens) of the mathematical axiom system of the displacement group. The elements of the displacement group are independent and complet entities with respect to the axiom system of the group. But, by analysing the subgroups of the displacement group (common to geometries with constant curvature) one transformes the variables of the axiom system in ‘places’ whose ‘objects’ lack any ontological commitment except with respect to the specified axioms. <br />
In general, a structure R is interpreted as a second order relation which is exemplified by (axiomatic) systems according to the pragmatic maxim of Charles Sanders Peirce.<br />
<br />
<br />
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<br />
=== Friday, February 10th at 2pm (tea and cookies at 1:30pm) ===<br />
<br />
==== ''Speaker:'' '''Natalie Paquette, Burke Fellow, Walter Burke Institute of Theoretical Physics at CalTech''' ====<br />
<br />
''Title:'' '''Moonshine: Old and New'''<br />
<br />
''Abstract: '' The whimsically-named Monstrous Moonshine is a mathematical story born in the late 1970's, which provided startling connections between two fundamental objects in mathematics. It eventually found an explanatory framework in the physics of an exotic solution of string theory. Starting in 2010, moonshine phenomena reemerged in the context of a more conceptually and physically central corner of string theory. In this talk, I will survey both old and new developments in moonshine with an emphasis on their physical meanings, and highlight the as-yet mysterious connections between the many beautiful mathematical and physical objects at play. I will summarize recent work clarifying these moonshine structures in string theory.<br />
<br />
<br />
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<br />
=== Monday, February 6th to Saturday, February 11 ===<br />
<br />
==== ''Speaker:'' '''9th ANNUAL CECAT WORKSHOP IN POINTFREE MATHEMATICS''' ====<br />
<br />
''Title:'' '''9th ANNUAL CECAT WORKSHOP IN POINTFREE MATHEMATICS'''<br />
<br />
''Abstract: '' Talks in Von Neumann Hall throughout the week.<br />
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<br />
=== Friday, February 3rd at 4pm (tea and cookies at 3:30pm) ===<br />
<br />
==== ''Speaker:'' '''Dr. Alberto Fernandez-Nieves, Professor of soft condensed matter physics at Georgia Tech''' ====<br />
<br />
''Title:'' '''Active nematics on tori'''<br />
<br />
''Abstract: '' We will discuss our recent results with active nematics on toroidal surfaces. We will first<br />
briefly describe how we generate and stabilize an otherwise unstable toroidal drop. We<br />
use these droplets to study the interplay between nematic order, geometry and<br />
topology. We find defect unbinding and defect-curvature coupling, consistent with<br />
theoretical expectations for inactive ordered materials arranged on the surface a torus.<br />
In our experiments, however, the number of defects is far larger than what one would<br />
expect for inactive nematics. This brings about interesting analogies with what we could<br />
call the high-temperature limit of inactive nematic liquid crystals.<br />
<br />
<br />
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<br />
=== Monday, January 9th at 4pm (tea and cookies at 2:30pm) ===<br />
<br />
==== ''Speaker:'' '''Professor Uwe Kahler, Universidade de Aveiro, Portugal''' ====<br />
<br />
''Title:'' '''Riemann-Hilbert problems in Clifford analysis'''<br />
<br />
''Abstract: '' One of the classic topics in Complex Analysis is the question of boundary value problems for holomorphic functions, so-called Riemann-Hilbert problems. This is not only for pure inner mathematical reasons, but also for its many applications, ranging from Materials with Memory, Inverse Scattering problems, to Statistical Physics. Due to its easy applicability since the beginning the question of Riemann-Hilbert problems in higher dimensions has caught the interest of many mathematicians. But there are essential differences between the two-dimensional case and the higher-dimensional case. In this talk we will present the general framework and highlight the difference between the two cases. Several open problems in the framework of hypercomplex analysis are being discussed.<br />
<br />
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<br />
=== Monday, January 9th at 3pm (tea and cookies at 2:30pm) ===<br />
<br />
==== ''Speaker:'' '''Professor Paula Cerejeiras, Universidade de Aveiro, Portugal''' ====<br />
<br />
''Title:'' '''Applications of Monogenic Wavelets to Image Processing '''<br />
<br />
''Abstract: '' We present an overview of applications of Clifford analysis to problems in image processing. As Clifford analysis techniques are strongly linked to the geometry of the underlying space it has generate an increasing interest in its applications to analytic signals in the last decade. Motivated by the problem of edge detection we introduce the concept of monogenic signal and discuss appropriate wavelet frames for it. We will finalize with a discussion on the group theoretical approach.<br />
<br />
<br />
----</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=MPC_Seminar_2018&diff=6MPC Seminar 20182021-02-22T18:29:50Z<p>Jipsen: Created page with " == Fall 2018 == Seminar organizer: Mihaela Vajiac The seminar talks are held in Keck Center for Science and Engineering, KC 171 (Center St. Orange, CA 92866, intersection o..."</p>
<hr />
<div><br />
== Fall 2018 ==<br />
<br />
Seminar organizer: Mihaela Vajiac<br />
<br />
The seminar talks are held in Keck Center for Science and Engineering, KC 171 (Center St. Orange, CA 92866, intersection of Center St. And Sycamore St.).<br />
Sometimes there will be a change of venue and the announcement will reflect this change.<br />
<br />
See [http://www.chapman.edu/discover/maps-directions/index.aspx Maps<br />
and directions], Keck Center is Building 28 on the Campus Map [https://www.chapman.edu/about/_files/maps-and-directions/current-maps/campus-map.pdf <br />
Campus map]<br />
<br />
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<br />
=== Thursday, December 6th 2018 at 4:15pm, in Keck 171, tea and cookies at 3:45pm in Keck 370===<br />
<br />
==== ''Speaker:'' ''' Dr. Bogdan Suceava, CSUF ''' ====<br />
<br />
''Title:'' ''' Strictly Convex Hypersurfaces Satisfying Weingarten-Type Inequalities '''<br />
<br />
''Abstract: '' Linear Weingarten surfaces in three-dimensional ambient space satisfy a relation between mean curvature and Gaussian<br />
curvature: aH^2+bK=c. We investigate whether for hypersurfaces invariant to inversions of dimensions 3, 4, and 5, there are<br />
curvature inequalities similar to the classical Weingarten condition. We also consider the globalization of these pointwise<br />
inequalities. This question is suggested by the investigations of Bang-Yen Chen’s fundamental inequalities, as we reflect<br />
on the geometric interpretations of these relations.Additionally, we plan to discuss other related inequalities, investigated in recent<br />
works written with Mihaela Vajiac, Nicholas Brubaker, and Leonard Giugiuc, respectively.<br />
<br />
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<br />
=== Friday, November 30th 2018 at 2:00pm, in Keck 171, tea and cookies at 1:30pm in Keck 370===<br />
<br />
==== ''Speaker:'' ''' Dr. Apostolos Tzimoulis, Chapman University postdoc ''' ====<br />
<br />
''Title:'' ''' Proof theory and algebraic semantics for predicate logics '''<br />
<br />
''Abstract: '' I will start with recasting classical first-order logic in an algebraic and proof-theoretic framework based on Lawvere's theory of hyperdoctrines. Then I will discuss the problem of obtaining general semantics for predicate non-classical logics, provide some examples, and argue that algebraic and proof-theoretic insight can help us understand better and solve this problem.<br />
<br />
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<br />
=== Thursday, November 29th 2018 at 4:15pm, in Keck 171, tea and cookies at 3:45pm in Keck 370===<br />
<br />
==== ''Speaker:'' ''' Dr. Sabine Hossenfelder (Frankfurt Institute for Advanced Studies)''' ====<br />
<br />
''Title:'' ''' Do women get fewer citations than men? '''<br />
<br />
''Abstract: '' I will talk about the results of a citation analysis on<br />
publication data from the arXiv and inspire in which we explored gender<br />
differences. I will further explain how we can use bibliometric analysis<br />
to improve the efficiency of knowledge discovery.<br />
<br />
<br />
There is also a public talk at 7pm, See [https://www.facebook.com/events/2293901217497764/ Public Talk, Argyros Forum, 7pm]<br />
<br />
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<br />
=== Conference: Monday to Friday, November 12th to November 16th in Sandhu Conference Center ===<br />
<br />
==== ''Speaker:'' ''' Advances in operator theory with applications to mathematical physics ''' ====<br />
<br />
''CONFERENCE:'' ''' Advances in operator theory with applications to mathematical physics '''<br />
<br />
''Abstract: '' For a complete schedule, and a list of abstracts, see: [http://www1.chapman.edu/~alpay/conf2018/conf2018.html Conference Webpage].<br />
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<br />
=== Monday, November 5th 2018 at 4:15pm, in Keck 171, tea and cookies at 3:45pm in Keck 370===<br />
<br />
==== ''Speaker:'' ''' Dr. Uwe Kahler, Universidade de Aveiro, ''' ====<br />
<br />
''Title:'' ''' Curvature detection using Taylorlets '''<br />
<br />
''Abstract: '' The problem in detection of nodules in medical images consists of two parts: the detection of edges and the detection of curvature. For the detection of edges as elements of the wavefront set of an image shearlets appeared in the last decade as the principal approach based on approximation. But elements of the wavefront set have a problem in the sense that they are singularities with prescribed direction, but not prescribed curvature. To overcome this problem higher order shearlets, so-called Taylorlets were introduced. While we will discuss them in this talk we will also point out and discuss a principal mathematical problem arising in their application: the problem of construction of a Schwartz function with infinitely many generalized vanishing moments. We will show that Meyer’s frequency-based approach does not fit this case and provide a space-based method for its generation.<br />
<br />
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<br />
=== Thursday, November 1st 2018 at 4:15pm, in Keck 171, tea and cookies at 3:45pm in Keck 370===<br />
<br />
==== ''Speaker:'' ''' Dr. Roman Buniy, Chapman University ''' ====<br />
<br />
''Title:'' ''' Tripartite entanglement of qudits '''<br />
<br />
''Abstract: '' We provide an in-depth study of tripartite entanglement of qudits. We start with a short review of tripartite entanglement invariants, prove a theorem about the complete list of all allowed values of three (out of<br />
the total of four) such invariants, and give several bounds on the<br />
allowed values of the fourth invariant. After introducing several<br />
operations on entangled states (that allow us to build new states from<br />
old states) and deriving general properties pertaining to their<br />
invariants, we arrive at the decomposition theorem as one of our main<br />
results. The theorem relates the algebraic invariants of any<br />
entanglement class with the invariants of its corresponding components<br />
in each of its direct sum decompositions. This naturally leads to the<br />
definition of reducible and irreducible entanglement classes. We<br />
explicitly compute algebraic invariants for several families of<br />
irreducible classes and show how the decomposition theorem allows<br />
computations of invariants for compounded classes to be carried out<br />
efficiently. This theorem allows us to compute the invariants for the<br />
infinite number of entanglement classes constructed from irreducible<br />
components. We proceed with the complete list of the entanglement<br />
classes for three qutrits with decompositions of each class into<br />
irreducible components, and provide a visual guide to interrelations of<br />
these decompositions. We conclude with numerous examples of building<br />
classes for higher spin qudits.<br />
<br />
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<br />
=== Friday, October 26th at 3:00pm, in Keck 171, tea and cookies at 2:30pm in Keck 370 ===<br />
<br />
==== ''Speaker:'' ''' Dr. Askery Canabarro, Federal University of Alagoas - BRAZIL ''' ====<br />
<br />
''Title:'' ''' Statistical and Machine Learning for physicists, but not just Physics (part 2) '''<br />
<br />
''Abstract: '' Machine Learning has become one of the most exciting areas of modern research and application. In these talks we provide an introduction to the core concepts and tools of machine learning in a way easily understood and intuitive to physicists. The review begins by covering fundamental concepts in ML and modern statistics such as overfitting, regularization, and generalization before moving on to more advanced topics in both supervised and unsupervised learning, for instance: ensemble deep learning, auto ML and so on. We illustrate the ideas with problems we are currently involved in. <br />
<br />
<br />
Part 2 of a series of 2 talks.<br />
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<br />
=== Thursday, October 25th at 4:15pm, in Keck 171, tea and cookies at 3:45pm in Keck 370 ===<br />
<br />
==== ''Speaker:'' ''' Dr. Askery Canabarro, Federal University of Alagoas - BRAZIL ''' ====<br />
<br />
<br />
''Title:'' ''' Statistical and Machine Learning for physicists (part 1) '''<br />
<br />
''Abstract: '' Machine Learning has become one of the most exciting areas of modern research and application. In these talks we provide an introduction to the core concepts and tools of machine learning in a way easily understood and intuitive to physicists. The review begins by covering fundamental concepts in ML and modern statistics such as overfitting, regularization, and generalization before moving on to more advanced topics in both supervised and unsupervised learning, for instance: ensemble deep learning, auto ML and so on. We illustrate the ideas with problems we are currently involved in. <br />
<br />
<br />
Part 1 of a series of 2 talks.<br />
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<br />
=== Friday, October 19th at 1:00pm, in Keck 171, tea and cookies at 2:00pm in Keck 370 ===<br />
<br />
==== ''Speaker:'' ''' Dr. Erik Linstead, Chapman University ''' ====<br />
<br />
''Title:'' ''' A Convoluted Talk '''<br />
<br />
''Abstract: '' Convolutional neural networks (CNNs) represent the current state-of-the-art in machine learning for computer vision. In this talk we will discuss some interesting applications of CNNs to non-traditional domains, as well as explore what happens to CNNs when we ignore computational efficiency to more closely align with neural physiology.<br />
<br />
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=== Thursday, October 18th at 4:15pm, in Keck 171, tea and cookies at 3:45pm in Keck 370 ===<br />
<br />
==== ''Speaker:'' ''' Dr. Sandu Popescu, IQS, Chapman University ''' ====<br />
<br />
''Title:'' ''' Dynamical quantum non-locality '''<br />
<br />
''Abstract: '' During the 50 years since its discovery, the Aharonov–Bohm effect has had a significant impact on the development of physics. Its arguably deepest implication, however, has been virtually ignored.<br />
<br />
Next year will be the 60th anniversary of the discovery of the Aharonov–Bohm (AB) effect, one of the most surprising and quintessential effects in quantum mechanics. Since its discovery in 1959, the AB effect has made a significant impact on the development of physics. It has been generalized in a variety of directions — from a rather straightforward dual effect such as the Aharonov–Casher effect, to the celebrated Berry phase, to non-Abelian gauge theories, to Wilson loops, to anyons. During these past 60 years the impact of the AB effect has been significant indeed.<br />
<br />
And during all these past 60 years, what I believe to be by far the deepest implication of the AB effect (discovered by Yakir Aharonov and described in his Tel Aviv University lecture notes and elsewhere) has been virtually ignored. It is an implication that transcends the specific context from which it originates, and goes directly to the very core of quantum physics: the quantum equations of motion are non-local. Without appreciating this fact, it is safe to say that no real understanding of the nature of quantum mechanics is possible.<br />
<br />
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<br />
=== Thursday, October 4th at 4:15pm, in Keck 171, tea and cookies at 3:45pm in Keck 370 ===<br />
<br />
==== ''Speaker:'' ''' Dr. Justin Dressel, Chapman University ''' ====<br />
<br />
''Title:'' ''' Strengthening weak measurements for qubit tomography and multitime correlators '''<br />
<br />
''Abstract: '' We re-examine the measurement strength needed to perform two recent quantum information tasks with qubits: state tomography using weak values, and determining multitime correlators. Traditionally these protocols have required weak measurements that are minimally disturbing, meaning that the coupling between an investigated quantum system and a measurement device has no appreciable influence on the evolution of the system. We show that the weakness of the interaction is not in fact necessary when measuring qubits. For the case of state tomography, we report an experiment performed with neutron matter-waves that extends the notion of generalized eigenvalues for the neutron's path system to allow the exact determination of weak values using both strong and weak interactions. Experimental evidence is given that strong interactions outperform weak ones both for precision and accuracy. For the case of obtaining multitime correlators, we show a method that uses sequential generalized measurements. Specifically, if a correlator can be expressed as an average of nested (anti)commutators of operators that square to the identity, then that correlator can be determined exactly from the average of a measurement sequence of arbitrary strength. We show that both two-point and four-point (out-of-time-ordered) correlators belong to this useful class of qubit correlators.<br />
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=== Thursday, September 27th at 4:15pm, in Keck 171, tea and cookies at 3:45pm in Keck 370 ===<br />
<br />
==== ''Speaker:'' ''' Dr. Matthew Leifer, Chapman University''' ====<br />
<br />
''Title:'' ''' Fine Tunings and the Nature of Quantum Reality '''<br />
<br />
''Abstract: '' Despite many years of research, there is still no universally agreed upon realist interpretation of quantum theory. In this talk, I argue that the main problem is to deal with the fine-tunings implied by no-go theorems about realist approaches to quantum theory, such as Bell’s theorem. We should seek to either eliminate these fine tunings or explain them as emergent. I will give an overview of the various fine-tunings that exist in quantum theory, due to nonlocality, contextuality, lack of time-symmetry, and results on the reality of the quantum state. I will explain how we can quantify each fine tuning, and exploit them in quantum information processing tasks. If time permits, I will outline two approaches to solve the fine-tuning problem based on block universe models with retrocausality and many-worlds.<br />
<br />
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<br />
=== Tuesday, September 18th at 4:15pm in Keck 171, tea and cookies at 3:45pm in Keck 370 ===<br />
<br />
==== ''Speaker:'' ''' Professor H. Turgay Kaptanoglu, Department of Mathematics, Bilkent University, Ankara ''' ====<br />
<br />
''Title:'' ''' Singular Integral Operators With Bergman-Besov Kernels on the ball '''<br />
<br />
''Abstract: '' Although the boundedness of the Bergman-Besov projection operators from Lebesgue classes onto Bergman-Besov spaces has been studied for several decades, the study of the boundedness of the same operators as singular integral operators between different Lebesgue classes are rather new. Some initial work has recently been done by Cheng, Fang, Wang, Yu for the weighted Bergman operator on the unit disc and by Cheng, Hou, Liu for the Drury-Arveson operator. Also Zhao has investigated certain sub-cases of the same problem as Bergman projections. The methods they employ are sporadic and specific to the particular cases they are interested in.<br />
<br />
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=== The 4th SYSMICS Workshop: Friday-Monday, September 14-17, in Sandhu Conference Center D1 ===<br />
<br />
==== ''Speaker:'' ''' The 4th SYSMICS Workshop ''' ====<br />
<br />
''Title:'' ''' Topic of the workshop: "Duality in Algebra and Logic” '''<br />
<br />
''Abstract: '' Workshop Webpage: http://math.chapman.edu/~jipsen/sysmics/<br />
<br />
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=== Friday, August 31st at 3:30pm, in Beckman 404 ===<br />
<br />
==== ''Speaker:'' ''' Dr. Philip Mannheim, Professor of Physics, University of Connecticut ''' ====<br />
<br />
''Title:'' ''' The Crisis in Fundamental Physics '''<br />
<br />
''Abstract: '' Cosmology deals with the the astrophysical macroscopic universe on large<br />
scales while fundamental physics deals with the particle physics<br />
microscopic universe on small ones. Recently it has become apparent that<br />
large and small scale physics are actually intertwined leading to an<br />
astro-particle picture of the universe. At the present time this picture<br />
has achieved great success, but at the same time it has led to many open<br />
questions and challenges, challenges which threaten to potentially<br />
undermine the entire picture. These challenges include dark matter, dark<br />
energy, the cosmological constant problem, quantum gravity, the status of<br />
supersymmetry, the multiverse picture, extra space-time dimensions, and the nature of the Higgs boson. In this talk we review these issues and suggest that their resolution would require a paradigm shift in our view of the universe.<br />
<br />
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=== Friday, August 31st at 1:00pm, Keck 171, lunch with the speaker in the Faculty Club at noon ===<br />
<br />
==== ''Speaker:'' ''' Dr. Philip Mannheim, Professor of Physics, University of Connecticut ''' ====<br />
<br />
''Title:'' ''' Why physicists are interested in differential geometry '''<br />
<br />
''Abstract: '' Ever since Einstein's development of gravity theory, general relativity and differential geometry have been central components of physics research and of our understanding of the universe. Of special interest is how gravity can interface with the other fundamental forces, the nuclear force, the weak force, and especially the electromagnetic force. In this talk we describe some of the motivation and central achievements for general relativity, and discuss some proposed generalizations of it such as torsion and Weyl geometry that might lead to a purely geometric unification of the fundamental forces.<br />
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=== Thursday, August 30th at 4:00pm, Keck 171, tea and cookies at 3:30pm in Keck 370===<br />
<br />
==== ''Speaker:'' ''' Dr. Philip Mannheim, Professor of Physics, University of Connecticut ''' ====<br />
<br />
''Title:'' ''' Quantum Conformal Gravity '''<br />
<br />
''Abstract: '' Conformal symmetry is a natural symmetry in physics since it is the full symmetry of the light cone. If all particles are to get their masses by symmetry breaking then conformal symmetry is the symmetry of the unbroken Lagrangian. Like Yang-Mills theories conformal symmetry has a local extension, namely conformal gravity, a pure metric-based candidate alternative to the non-conformal invariant standard Newton-Einstein theory of gravity. With its dimensionless coupling constant quantum conformal gravity is power counting renormalizable. Since its equations of motion are fourth-order derivative equations conformal gravity has long been thought to possess unacceptable ghost states of negative norm that would violate unitarity. However on constructing the quantum Hilbert space Bender and Mannheim found that this not to be the case. Conformal gravity is thus offered as a completely consistent and unitary quantum theory of gravity, one that requires neither the extra dimensions nor the supersymmetry of string theory. As formulated via local conformal invariance there is no intrinsic classical gravity, with gravity instead being intrinsically quantum-mechanical, with the observed classical gravity being output rather than input. The contribution of the graviton loops of conformal gravity enables conformal gravity to solve the cosmological constant problem. Like Yang-Mills the potential of conformal gravity contains both a Newtonian term and a linear potential. Together with a quadratic potential that the theory also contains conformal gravity is able to explain the systematics of galactic rotation curves without any need for galactic dark matter. Since all mass is to be dynamical there cannot be a fundamental double-well Higgs potential in the theory. Instead, the Higgs boson is generated dynamically, with the hierarchy problem then being solved.<br />
<br />
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=== Thursday, August 23rd at 4:00pm, Keck 171, tea and cookies at 3:30pm in Keck 370===<br />
<br />
==== ''Speaker:'' ''' Dr. Gunduz Caginalp, Professor of Mathematics, University of Pittsburgh''' ====<br />
<br />
''Title:'' ''' Volatility Maxima as a Forecaster of Trading Price Extrema '''<br />
<br />
''Abstract: '' This is joint work with Carey Caginalp. The relationship between price volatility and a market extremum is examined using a fundamental economics model of supply and demand. By examining randomness through a microeconomic setting, we obtain the implications of randomness in the supply and demand, rather than assuming that price has randomness on an empirical basis. Within a very general setting the volatility has a maximum that precedes the extremum of the price. A key issue is that randomness arises from the supply and demand, and the variance in the stochastic differential equation governing the logarithm of price must reflect this. Analogous results are obtained by further assuming that the supply and demand are dependent on the deviation from fundamental value of the asset.<br />
<br />
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<br />
== Spring 2018 ==<br />
<br />
----<br />
<br />
The seminar talks are in Von Neumann Hall VN 116 (545 W Palm Ave<br />
corner of W Palm Ave and railroad, Orange, CA 92866).<br />
Sometimes there will be a change of venue and the announcement will reflect this change.<br />
<br />
See [http://www.chapman.edu/discover/maps-directions/index.aspx Maps<br />
and directions], Von Neumann Hall is Building 48 on the Campus Map [https://www.chapman.edu/about/_files/maps-and-directions/current-maps/campus-map.pdf <br />
Campus map]<br />
<br />
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=== Friday, May 11th at 3:00pm, Von Neumann Hall, tea and cookies at 2:30pm ===<br />
<br />
==== ''Speaker:'' ''' Dr. Nadia Ahmed, Saddleback''' ====<br />
<br />
''Title:'' ''' Consumer-centric Residential Demand Side Management '''<br />
<br />
''Abstract: '' Energy Management Systems (EMS) are mainly price driven with minimal consumer interaction. To improve the effectiveness of EMS in the context of demand response, an alternative EMS control framework driven by resident behavior patterns is developed. Using hidden Markov modeling techniques, the EMS detects consumer behavior from real-time aggregate consumption and a pre-built dictionary of reference models. These models capture variations in consumer habits as a function of daily living activity sequence. Following a training period, the system identifies the best fit model which is used to estimate the current state of the resident. When a request to activate a time-shiftable appliance is made, the control agent compares grid signals, user convenience constraints, and the current consumer state estimate to predict the likelihood that the future aggregate load exceeds a consumption threshold during the operating cycle of the requested device. Based on the outcome, the control agent initiates or defers the activation request. In an extension of this work, a battery health conscious stochastic dynamic programming control framework is introduced as part of a greater cyber physical system which incorporates the harvesting unit, the storage unit, the residential load profile, the weather, the weather forecast, the utility, and consumer preferences into a unified Markov decision process.<br />
<br />
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=== IQS Live Podcast, Monday, April 16th at 6:00pm, 1888 Center, 115 North Orange Street ===<br />
<br />
==== ''Speaker:'' ''' Adam Becker''' ====<br />
<br />
''Title:'' ''' What Is Real? The Unfinished Quest for the Meaning of Quantum Physics'''<br />
<br />
''Abstract: '' IQS Live podcast recording and book signing with Adam Becker, author of:<br />
<br />
"What Is Real? The Unfinished Quest for the Meaning of Quantum Physics”<br />
<br />
Monday April 16<br />
6pm-8pm<br />
1888 Center, 115 North Orange Street, Orange, CA 92866<br />
<br />
Produced in partnership with the Institute for Quantum Studies, Chapman University<br />
<br />
<br />
Organized by IQS. Free admission, but seating is limited so you have to RSVP at the following link: <br />
[https://bit.ly/AdamBecker Event Registration]<br />
<br />
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=== Friday, April 13th at 3:30pm, Von Neumann Hall, tea and cookies at 3:00pm ===<br />
<br />
==== ''Speaker:'' ''' Dr. Jose Raul Gonzalez Alonso, Chapman University''' ====<br />
<br />
''Title:'' ''' Quantum Chaos, Information Scrambling, and Out-of-time-ordered Correlators '''<br />
<br />
''Abstract: '' Out-of-time-ordered-correlators (OTOCs) have emerged as a useful tool to study quantum chaos and the scrambling and delocalization of information in many-body systems. While challenging, their experimental measurement has been achieved in NMR, trapped ion, and superconducting systems. In this talk, I will review the different open problems at the intersection of quantum chaos, information scrambling, and OTOCs and the recent progress in solving them.<br />
<br />
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=== Friday, April 6th Sixth annual Computational and Data Sciences Graduate Conference ===<br />
<br />
==== ''Speaker:'' ''' Chapman University Graduate Students, 9:15am - 4:30pm, Argyros Forum 209ABC''' ====<br />
<br />
''Title:'' ''' Sixth annual Computational and Data Sciences Graduate Conference'''<br />
<br />
''Abstract: '' Various<br />
<br />
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=== Friday, March 30th at 3:00pm, Von Neumann Hall ===<br />
<br />
==== ''Speaker:'' ''' Kai-Wen Tu, Chapman University''' ====<br />
<br />
''Title:'' ''' Fourier Transform and Signal Processing Application with a SAR Imaging Example'''<br />
<br />
''Abstract: '' In solving heat-flow problems Fourier found that a periodic function can be represented by an infinite series of sinusoidal functions. Generalization from Fourier Series to Fourier Transform and its discrete form, the Discrete Fourier Transform (DFT) will be discussed briefly. Development of a computationally efficient algorithm FFT (Fast Fourier Transform) for computing DFT will be described with MATLAB illustration.<br />
The second part of the talk will focus on a specific signal processing application using FFT. An overview of imaging radar systems with conventional aperture as well as with synthetic aperture (SAR) will be given. Image resolution will be shown to be related to pulse compression and synthetic array processing as the antenna beam creates a footprint with the continuing illumination of a designated spot. Image formation of the Spotlight imaging mode encompassing signal data collection, motion compensation, data sampling, range dechirp, azimuth compression, polar interpolation, 2-D FFT, phase correction, and pixel magnitude encoding will be presented.<br />
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=== Tuesday, March 20th at 3:00pm, Von Neumann Hall ===<br />
<br />
==== ''Speaker:'' ''' Mic Detlefsen, University of Notre Dame ''' ====<br />
<br />
''Title:'' ''' Some Elements of Hilbert’s Formalism '''<br />
<br />
''Abstract: '' The aim of this talk is to describe and consider the significance of a certain element of Hilbert¹s formalist viewpoint that I call its descriptive or observational element. This element played an important role in shaping Hilbert¹s distinctive approach to the consistency problem for arithmetic (and to other consistency problems). It seems not to have been generally well recognized and appreciated. <br />
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=== Friday, March 16th at 3:00pm, Von Neumann Hall ===<br />
<br />
==== ''Speaker:'' ''' Lorenzo Catani, UCL ''' ====<br />
<br />
''Title:'' ''' Csirelson’s bounds as a refinement of Landauer’s principle '''<br />
<br />
''Abstract: '' I will present a simple single qudit protocol that computes a non-linear function. It consists of a system in a fixed state, two gates controlled by classical dits (d-level systems) and a fixed measurement. The goal is to choose gates to optimise the average probability over all input combinations of dits to obtain the target non-linear function as output. <br />
<br />
I will show that any strategy in the single-qudit protocol can be mapped to a strategy in a two qudits CHSH game, thus obtaining the known classical Bell bounds for the strategies that only involve classical reversible computation or quantum stabiliser computation, and Csirelson’s bounds for general quantum strategies. Since the single qudit protocol restricts the degrees of freedom to gates only, we analyse the bounds obtained in light of Landauer’s principle, showing that there is a trade-off in entropic cost versus increased success probability. The single qubit computation can perform better than the reversible bit computation, but it cannot achieve the performance of the irreversible computation. In this sense the protocol acts as an irreversibility witness. In the case of systems of dimension two (bits and qubits) these results have a clear geometric interpretation in the corresponding state spaces. <br />
<br />
I will briefly discuss how our scheme also acts as a dimensional witness and I will conclude with some comments on the sources of non-classicality present in the current protocol since non-locality and contextuality (in its standard notions) are not present.<br />
<br />
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=== Friday, March 9th at 3:00pm, Von Neumann Hall ===<br />
<br />
==== ''Speaker:'' ''' Dr. Carey Caginalp, University of Pittsburgh ''' ====<br />
<br />
''Title:'' ''' Supply, Demand, Volatility and Fat Tails '''<br />
<br />
''Abstract: '' The classical equations of mathematical finance involve basic assumptions that are convenient mathematically and are essentially a particular limit of the underlying market phenomena. The assumptions involve infinite capital for arbitrage and independent Gaussian increments in relative price change. Among the consequences are an exponential decay in large deviations of relative price and volatility that is essentially constant in time. We use a basic supply/demand model to explain the fat tails phenomena based on endogenous reasons. The bubble in cryptocurrencies can also be explained in terms of this approach in which the liquidity price, namely, cash available for investing in a particular asset divided by the number of units available. Current work is focused on demonstrating that the extrema in price are accompanied by extrema in volatility.<br />
(Research in collaboration with Dr. Carey Caginalp) <br />
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=== IQS Workshop: Saturday, March 3rd, Argyros Forum 212 ===<br />
<br />
==== ''Speaker:'' ''' Quantum Simulation and Quantum Walks Workshop ''' ====<br />
<br />
''Title:'' ''' Quantum Simulation and Quantum Walks Workshop '''<br />
<br />
''Abstract: '' Organized by IQS. For registration to this event please follow the link: [https://events.chapman.edu/43566 Event Registration].<br />
<br />
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=== IQS Workshop: Thursday-Friday, March 1st and 2nd, Beckman Hall 404 ===<br />
<br />
==== ''Speaker:'' ''' AAV Anniversary Conference - Celebrating 30 Years of Weak Values ''' ====<br />
<br />
''Title:'' ''' AAV Anniversary Conference - Celebrating 30 Years of Weak Values '''<br />
<br />
''Abstract: '' Organized by IQS. For registration to this event please follow the link: [https://events.chapman.edu/44046 Event Registration].<br />
<br />
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=== Friday, February 23rd at 3:00pm, Von Neumann Hall ===<br />
<br />
==== ''Speaker:'' ''' Dr. Ken Wharton, San Jose State ''' ====<br />
<br />
''Title:'' ''' Spacetime-Based Retrocausal Models '''<br />
<br />
''Abstract: '' Ordinary quantum states grow exponentially with particle number, and cannot exist as a function on ordinary spacetime. But when retrocausal models are considered, the reason for this exponential growth disappears, raising the exciting prospect of some ontic description of quantum phenomena that does exist in spacetime. (In such models the spacetime-based ontic parameters need only work for the actual future measurement setting, not all possible counterfactual settings.) I will give a detailed example of such a model, which can properly account for all maximally-entangled two-qubit states. The key is an "all at once" analysis of the histories, rather than a dynamical evolution of instantaneous states. Intriguingly, the model naturally supplies a novel alternate interpretation of Weak Values.<br />
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=== Thursday, February 22nd at 4:00pm, Von Neumann Hall ===<br />
<br />
==== ''Speaker:'' ''' Adam Becker, Science Writer ''' ====<br />
<br />
''Title:'' ''' Myths about the history of the de Broglie-Bohm interpretation: setting the record straight '''<br />
<br />
''Abstract: '' Misconceptions about the de Broglie-Bohm interpretation of quantum mechanics appeared immediately at its first public presentation by de Broglie at Solvay in 1927. It took many years for those misconceptions to fall away. Today, we finally have a good understanding of the theory (or at least a better understanding), but there are still many common misconceptions about its history. What were the nature of the objections to de Broglie's version of the interpretation at Solvay? Why did de Broglie abandon it? What prompted Bohm to look for a new interpretation 25 years later? How were Bohm's ideas received by his contemporaries? And why did Bohm himself ultimately abandon his own ideas for another quarter of a century? There are "standard" answers to these questions, most of which are simply myths. For example, Pauli did not stump de Broglie at Solvay, Oppenheimer was generally kind to Bohm during his time on the blacklist, and Bohm's ideas were not simply ignored or dismissed out of hand by his contemporaries. In my talk, I will discuss the origins of these myths, and the far more complicated and surprising historical truths that they obscure.<br />
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=== Friday, February 16th at 3:00pm, Von Neumann Hall ===<br />
<br />
==== ''Speaker:'' ''' Eli Levenson-Falk, USC ''' ====<br />
<br />
''Title:'' ''' Fleas on Schrödinger's Cat: Quasiparticles in Superconducting Quantum Circuits '''<br />
<br />
''Abstract: '' Superconducting electrical circuits can be used for quantum computing, quantum simulation, ultra-low-noise amplification, and precision sensing. However, quasiparticles--electron-like single-particle excitations of the superconducting condensate--can cause loss and noise, limiting the performance of these devices. The generation mechanisms, behavior, and annihilation channels of these quasiparticles are still poorly understood, hindering efforts to eliminate them from circuits. I will review the evidence for different quasiparticle models, show measurements using Andreev bound states as quasiparticle traps, and discuss future experiments that will determine the best ways to mitigate the harmful effects of quasiparticles.<br />
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=== Friday, February 9th at 4:00pm, Beckman Hall 105 ===<br />
<br />
==== ''Speaker:'' ''' Dr. J.H. Eberly, Department of Physics and Astronomy, Center for Coherence and Quantum Optics, University of Rochester ''' ====<br />
<br />
''Title:'' ''' Hidden Coherences and Complementarity '''<br />
<br />
''Abstract: '' Interference, duality, polarization, coherence and entanglement are a partial list of notions that belong to both quantum physics and classical optics. It has been our recent goal to bring quantum-classical links into wider view and to indicate directions in which forthcoming and future work may be able to promote discussion and lead to a more unified understanding. A starting point has often been Niels Bohr's pronouncements and explanations of complementarity, as a way to come to grips with de Broglie's duality. Related debates have engaged and challenged philosophers as well as physicists for almost a century. Complemenn-classical world's mysterious quantum features. Disputed analyses and unresolved conflicts are still debated. It seems to have escaped notice that a key element in Bohr's own defining summary has never been captured in assessments to date. We will report what we believe to be the first description of complementarity that is quantitatively complete, along with experimental evidence of completeness.<br />
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=== Friday, February 9th, at 2:00pm in Hashinger 150 (Irvine Lecture Hall) ===<br />
<br />
==== ''Speaker:'' ''' Dr. Cumrun Vafa, Harvard University ''' ====<br />
<br />
''Title:'' ''' Fundamental Lessons From String Theory '''<br />
<br />
''Abstract: '' String theory has been developed for more than 40 years<br />
now but it seems that we are still far from its final formulation.<br />
Nevertheless, I explain some of the highlights of what we have learned<br />
from string theory and how it revolutionizes many of the fundamental<br />
principles of physics.<br />
<br />
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=== Thursday, February 8th, at 7:00pm in Beckman Hall 404 ===<br />
<br />
==== ''Speaker:'' ''' Dr. Cumrun Vafa, Harvard University ''' ====<br />
<br />
''Title:'' ''' Physics and Geometry '''<br />
<br />
''Abstract: '' This talk reviews the deep historical connections between geometry<br />
and physics. In modern times, the extra dimensions of string theory has provided a new<br />
opportunity for enhancing this interplay which will be illustrated by concrete examples.<br />
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=== Monday, February 5th at 4:00pm, Von Neumann Hall ===<br />
<br />
==== ''Speaker:'' ''' Dr. Ales Pultr, Charles University, Prague ''' ====<br />
<br />
''Title:'' ''' Point-free topology and some of its merits '''<br />
<br />
''Abstract: '' Point-free thinking, example. Points vs. (realistic) places.<br />
A glimpse of history: Synthetic and analytic geometry; classical topology as a generalized geometry is the analytic version of such a generalization. De- velopment starting in late 30ties and 40ties, how the point-free ideas connect with the classical ones (Hausdorff, Kuratowski, Caratheodory, Freudenthal). The break in the late fifties.<br />
Definition of a locale (frame). Basic concepts and how one works with them.<br />
One obtains a broader range of spaces and every generalization calls for justification. This will be done by discussing the following legitimate ques- tions.<br />
(1) Is the broader range of spaces desirable? Do we get in some sense a better theory and when?<br />
(2) Is the algebraic technique appropriate, does it not obscure the geomet- ric content?<br />
(3) Do we not lose to much information when abolishing points?<br />
We will start by briefly answering question (3) and then go to (1) and (2) presenting examples of results that are nicer, or cannot hold in the classical context at all. In particular we will emphasize the constructive aspects (facts working without choice principles, such as compactification, completion, or Stone duality - the last is so simple that it can serve also as an example of the advantage of the algebraic techniques).<br />
Note of the role of point-free topology in logic and theoretical computer science.<br />
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=== Monday, January 29th at 3:00pm, Von Neumann Hall, third session of the OCIE-HPML seminar ===<br />
<br />
==== ''Speaker:'' '''Dr. Jamie Tappenden (USC) ''' ====<br />
<br />
''Title:'' ''' Frege, Carl Snell and Romanticism; Fruitful Concepts and the 'Organic/Mechanical' Distinction '''<br />
<br />
''Abstract: '' A surprisingly neglected figure in Frege scholarship is the man Frege describes (with praise that is very rare for Frege) as his "revered teacher", the Jena physics and mathematics professor Carl Snell. It turns out that there is more of interest to say about Snell than can fit into one talk, so I'll restrict attention here to just this aspect of his thought: the role of the concept of "organic", and a contrast with "mechanical". Snell turns out to have been a philosophical Romantic, influenced by Schelling and Goethe, and Kant's Critique of Judgement. In Frege's environment, the "organic/mechanical" contrast, understood in a distinctively Romantic fashion, had reached the status of "accepted, recognized cliché". More generally, Frege's environment was more saturated with what we now call ``Continental philosophy" than we might expect. This context-setting has a payoff for our reading of Frege's texts: many expressions and turns of phrase in Frege that have been regarded as vague, throwaway metaphors turn out to be literal references to ideas that would have been salient among the people in Frege spent time with day-to-day. In particular, this is true of Frege's account of "extending knowledge" via "fruitful concepts" and his rejection of the idea that logic and mathematics can be done "mechanically" (as with Jevons' logic machines, or Fischer's "aggregative mechanical thought"). When Frege appealed to "organic connection" and speaks of fruitful concepts as containing conclusions "like a plant in its seeds", he would have expected his apparent metaphors to have been understood in a very specific way, as alluding to a recognized contrast between "organic" and "mechanical" connection that was applied by Snell and those close to him not only to distinctions between biological and physical reasoning but also to distinctions of types of reasoning in arithmetic and geometry. <br />
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=== Monday, January 29th at 4:00pm (Beckman Hall 404) ===<br />
<br />
==== ''Speaker:'' ''' Peter Coffee, Vice President for Strategic Research at salesforce.com ''' ====<br />
<br />
''Title:'' ''' The Future That's Already Happened: Fundamental Forces of Change'''<br />
<br />
''Abstract: '' There are two ways to talk about "the future." One involves making predictions of what might happen. The other, much less speculative, solves present-day equations for a future value of time. Today, the second approach can make use of observable facts about connection, collaboration, acceleration, and introduction of machine intelligence ("Ex Machination") into devices and processes -- to give us a crisp and compelling picture of what otherwise might seem wild-eyed visions. <br />
<br />
For registration to this event please follow the link: [https://events.chapman.edu/45114 Event Registration].<br />
<br />
<br />
----</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=MPC_Seminar_2019&diff=5MPC Seminar 20192021-02-22T18:28:52Z<p>Jipsen: Created page with " == Spring 2019 == The seminar talks are held in '''Keck Center for Science and Engineering, KC 171''' (Center St. Orange, CA 92866, intersection of Center St. And Sycamore S..."</p>
<hr />
<div><br />
== Spring 2019 ==<br />
<br />
The seminar talks are held in '''Keck Center for Science and Engineering, KC 171''' (Center St. Orange, CA 92866, intersection of Center St. And Sycamore St.), '''usually on Wednesday at 4 pm'''.<br />
Sometimes there will be a change of time or venue and the announcement will reflect this change.<br />
<br />
See [http://www.chapman.edu/about/maps-directions/index.aspx Maps<br />
and directions], Keck Center is Building 28 on the Campus Map [https://www.chapman.edu/about/_files/maps-and-directions/current-maps/campus-map.pdf <br />
Campus map]<br />
<br />
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=== Thursday, May 16, 2019 at 3 pm, in Keck 370, tea and cookies at 2:40pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Dr. Purbita Jana, The Institute of Mathematical Sciences, Chennai, India''' ====<br />
<br />
''Title:'' '''Intuitionistic topological systems and their connections with Heyting algebra and Gödel algebra'''<br />
<br />
''Abstract:'' (joint work with Antonio Di Nola and Revaz Grigolia) This talk will suggest a new approach of representation of a Heyting algebra as an I-topological system. I-topological systems will be introduced following the notion of topological system introduced by S. Vickers which is a triple (X, |=, A) consisting of a non-empty set X, a frame A and a relation between X and A satisfying logic of finite observations or geometric logic. It is well known that frame is the Lindenbaum algebra of geometric logic where as the Lindenbaum algebra of intuitionistic logic is a Heyting algebra. Hence to define I-topological systems, intuitionistic logic plays a crucial role. Moreover, we will focus on the categorical relationships between the I-topological system, Esakia space and Heyting algebra (and its particular case of Gödel algebra).<br />
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=== Tuesday, April 16, 2019 at 5 pm, in Keck 370, tea and cookies at 3:40pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Dr. Michele Piazzai, University of Amsterdam, Netherlands''' ====<br />
<br />
''Title:'' '''The Ecology of Ideas: Computational Evidence of Self-Organization'''<br />
<br />
''Abstract:'' Concepts are cognitive structures that people use to categorize objects and organize their knowledge of the world. Common examples include food and furniture, but also rock'n'roll, quantum physics, and blockchain. For individuals, concepts are the main tools of learning and inference; for groups of individuals (i.e., social systems), they are indispensable instruments of coordination and exchange. But how can the idiosyncratic knowledge of individuals in a social system converge on shared concepts, so as to allow coordination? Conventional wisdom in social science suggests that designated mediators, such as music critics, facilitate this convergence by endorsing the learning and usage of particular concepts. By contrast, I will argue that rational decisions embedded in everyday social interaction provide the necessary and sufficient conditions for concepts' convergence. No mediators are needed for the agents to develop a shared conceptual structure: as commonly occurs in complex adaptive systems, design emerges in the absence of centralized designers. Simulation results are presented that illustrate this point.<br />
<br />
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<br />
=== Thursday, April 11, 2019 at 4 pm, in Keck 370, tea and cookies at 3:40pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Dr. Michele Piazzai, University of Amsterdam, Netherlands''' ====<br />
<br />
''Title:'' '''The Ecology of Ideas: Empirical Evidence of Evolutionary Pressure'''<br />
<br />
''Abstract:'' Building on the notion that the collective cognition of agents engaged in social interaction constitutes a complex adaptive system, I present a theoretical framework to describe agents' shared conceptual structure as a self-replicating network of objects, ideas, and decisions. Finite cognitive resources at the agents' disposal create a competitive environment where concepts vie to be assigned to objects in categorization decisions, so as to survive in the agents' memory. This struggle for survival gives the socio-cognitive system traits characteristic of an ecology. I identify two sources of ecological interdependence among concepts, including horizontal relations between concepts located at the same level of abstraction and vertical relations between concepts located at different levels. An empirical model is developed to test whether these relations affect the selection of concepts in agents' decisions and the evolution of their shared conceptual structure. To test this model, I analyze one decade's worth of categorization decisions made by users of a crowd-sourced music encyclopedia whose objective is sorting records into genres and sub-genres.<br />
<br />
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<br />
=== Thursday, March 28, 2019 at 5 pm, in Keck 171, tea and cookies at 4:40pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Prof. Giovanni Sambin, University of Padova, Italy''' ====<br />
<br />
''Title:'' '''Half way to Grothendieck's aim (embedding of pointwise topology into pointfree topology)'''<br />
<br />
''Abstract:'' For a mathematician, the most interesting motivation for a different foundation is when it offers a new perspective or even a solution to an old problem. Developing topology over a very "weak" foundation offers a precise mathematical expression and proof to the expectation, which is well present since the time of Grothendieck, of a notion of space generalising that of topological space.<br />
The well-known link between pointfree and standard topology (with points) is a categorical adjunction between topological spaces Top and locales Loc. Using a "weak" foundation to develop topology, one is compelled to preserve more information than usual, and thus replace topological spaces with "concrete spaces", and locales with "positive topologies". Contrary to a common expectation, it is precisely this "useless" information what offers a solution to Grothendieck's aim. That is, the above adjunction becomes a categorical embedding of concrete spaces into positive topologies.<br />
This embedding does not look possible without exploiting the presence of the new (intrinsically existential) notion of positivity relation.<br />
Half way because this leaves the problem open of finding a suitable notion of positivity (formal closed subsets) in the framework of arbitrary Grothendieck topologies.<br />
<br />
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<br />
=== Wednesday, March 13, 2019 at 4 pm, in Keck 171, tea and cookies at 3:45pm in Keck 370 ===<br />
<br />
==== ''Speaker:'' '''Dr. Matt Pusey, University of Oxford''' ====<br />
<br />
''Title:'' '''Anomalous weak values and contextuality: robustness and imaginary<br />
parts'''<br />
<br />
''Abstract:'' I will discuss extensions to my previous work linking anomalous weak<br />
values with contextuality. In particular, I will show that using<br />
transformation noncontextuality obviates the experimentally<br />
problematic requirement that the post-selection is projective. I will<br />
also discuss the status of the imaginary part of weak values. My talk<br />
will be based on joint work with Ravi Kunjwal and Matteo Lostaglio:<br />
https://arxiv.org/abs/1812.06940<br />
<br />
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<br />
=== Wednesday, February 27, 2019 at 4 pm, in Keck 171, tea and cookies at 3:45pm in Keck 370 ===<br />
<br />
==== ''Speaker:'' '''Prof. Christos Tzounis, California State Polytechnic University, Pomona''' ====<br />
<br />
''Title:'' '''Metric of an Evaporating Black Hole'''<br />
<br />
''Abstract:'' We present an approximate time-dependent metric in ingoing Eddington-Finkelstein coordinates for an evaporating nonrotating black hole as a first-order perturbation of the Schwarzschild metric, using the linearized back reaction from a realistic approximation to the stress-energy tensor for the Hawking radiation in the Unruh quantum state.<br />
<br />
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<br />
=== Wednesday, February 13, 2019 at 4 pm, in Keck 171, tea and cookies at 3:45pm in Keck 370 ===<br />
<br />
==== ''Speaker:'' '''Prof. Peter Rakitzis, Institute of Electronic Structure and Laser, Heraklion, Greece''' ====<br />
<br />
''Title:'' '''Ultrahigh-Density Spin-Polarized H and D Atoms Observed via Magnetization Quantum Beats'''<br />
<br />
''Abstract:'' We measure nuclear and electron spin-polarized H and D densities of at least $10^{20}$ cm$^{−3}$ and $10^{19}$ cm$^{−3}$, i.e., at pressures of 5 bar and 0.5 bar, respectively, with ∼10-50 ns lifetimes, from the photodissociation of HBr and DI with circularly polarized UV light pulses. We observe the hyperfine quantum beating of the H and D magnetization with a pickup coil, i.e., the respective 0.7 and 3 ns periodic transfer of polarization from the electrons to the nuclei and back. These pulsed densities are ∼7 orders of magnitude higher than that produced by conventional continuous-production methods, and are sufficient for three novel applications: (a) laser-driven ion acceleration of spin-polarized electrons, protons, or deuterons, (b) the preparation of nuclear-spin-polarized molecules, and (c) the demonstration of spin-polarized D-T or D$^{-3}$He laser fusion at large laser facilities such as NIF, for which a reactivity enhancement of ∼50% is expected.<br />
<br />
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=== Tuesday, February 5 -- Saturday, February 9, 2019 in Keck 370 ===<br />
<br />
==== '''11th Annual Chapman University CECAT Workshop on Pointfree Mathematics''' ====<br />
<br />
TUESDAY, February 5th:<br />
<br />
1:00 - 2:00pm '''M. Andrew Moshier''', ''Chapman University'', Weakening relations<br />
<br />
THURSDAY, February 7th:<br />
<br />
10:30 - 11:30am: '''Peter Jipsen''', ''Chapman University'', Involutive residuated lattices and relation algebras<br />
<br />
11:30 - 12:30pm: '''Sara Vannucci''', ''University of Salerno'', Semiring and Semimodule Issues in Residuated Lattices<br />
<br />
1:00 - 2:15pm: '''Rick Ball''', ''University of Denver'', Pointfree Integration<br />
<br />
2:15 - 3:15pm: '''Anna Laura Suarez''', ''University of Birmingham'', D-frames and frame coproducts<br />
<br />
3:30 - 4.30pm: '''Alex Kurz''', ''Chapman University'', On the duality theory of weakening relations<br />
<br />
FRIDAY, February 8th<br />
<br />
10:30 - 11:30am: '''Ales Pultr''', ''Charles University'', Strong Hausdorff properties of frames<br />
<br />
11:30 - 12:30pm: '''Diego Valota''', ''University of Milan'', [http://math.chapman.edu/~jipsen/cecat/11th-Pointfree-Mathematics-Workshop/DiegoValota2019.pdf Computing Spectra via Dualities in the MTL hierarchy]<br />
<br />
2:00 - 3:00pm: '''Olim Tuyt''', ''University of Bern'', Algebraic finite model property of a modal Gödel logic<br />
<br />
3:00 - 4:15pm: '''Rick Ball''', ''University of Denver'', Pointfree Integration, continued<br />
<br />
SATURDAY, February 9th<br />
<br />
1:00 - 5:00pm: Discussion session<br />
<br />
<br />
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----</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=MPC_Seminar&diff=4MPC Seminar2021-02-22T18:27:57Z<p>Jipsen: Created page with "This is the homepage of the Chapman University '''Mathematics, Physics, and Computation Seminars''' (MPC Seminar) ''Seminar Organizers:'' Roman Buniy and Peter Jipsen =..."</p>
<hr />
<div>This is the homepage of the Chapman University '''Mathematics, Physics, and Computation Seminars'''<br />
([[MPC Seminar]])<br />
<br />
''Seminar Organizers:'' Roman Buniy and Peter Jipsen<br />
<br />
<br />
== Spring 2021 ==<br />
<br />
The MPC seminar is held via Zoom for now. The Zoom address will be sent in the email announcements.<br />
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<br />
<br />
=== Thursday, Jan 21st, 2021, 4 - 5 pm on Zoom ===<br />
<br />
==== ''Speaker:'' '''Mike Campbell, Eureka (SAP), joint work with Vernon Smith (Chapman University)''' ====<br />
<br />
''Title:'' '''An Elementary Humanomics Approach to Boundedly Rational Quadratic Models'''<br />
<br />
''Video of talk:'' [https://youtu.be/F74RlCAjC_A YouTube] ''Slides:'' [http://math.chapman.edu/~jipsen/seminarposters/MikeCampbell2021HumanomicsApproachBRQuadratic.pdf pdf]<br />
<br />
''Abstract:'' We take a refreshing new look at boundedly rational quadratic models in economics using some elementary modeling of the principles put forward in the book Humanomics by Vernon L. Smith and Bart J. Wilson. A simple model is introduced built on the fundamental Humanomics principles of gratitude/resentment felt and the corresponding action responses of reward/punishment in the form of higher/lower payoff transfers. There are two timescales: one for strictly self-interested action, as in economic equilibrium, and another governed by feelings of gratitude/resentment. One of three timescale scenarios is investigated: one where gratitude/resentment changes much more slowly than economic equilibrium ("quenched model"). Another model, in which economic equilibrium occurs over a much slower time than gratitude/resent evolution ("annealed model") is set up, but not investigated. The quenched model with homogeneous interactions turns out to be a non-frustrated spin-glass model. A two-agent quenched model with heterogeneous aligning (ferromagnetic) interactions is analyzed and yields new insights into the critical quenched probability p (1-p) that represents the empirical frequency of opportunity for agent i to take action for the benefit (hurt) of other that invokes mutual gratitude (resentment). A critical quenched probability p*i, i=1,2, exists for each agent. When p < p*i, agent i will choose action in their self-interest. When p > p*i, agent i will take action sensitive to their interpersonal feelings of gratitude/resentment and thus reward/punish the initiating benefit/hurt. We find that the p*i are greater than one-half, which implies agents are averse to resentful behavior and punishment. This was not built into the model, but is a result of its properties, and consistent with Axiom 4 in Humanomics about the asymmetry of gratitude and resentment. Furthermore, the agent who receives less payoff is more averse to resentful behavior; i.e., has a higher critical quenched probability. For this particular model, the Nash equilibrium has no predictive power of Humanomics properties since the rewards are the same for self-interested behavior, resentful behavior, and gratitude behavior. Accordingly, we see that the boundedly rational Gibbs equilibrium does indeed lead to richer properties.<br />
<br />
''Link to paper:'' [https://digitalcommons.chapman.edu/cgi/viewcontent.cgi?article=1330&context=esi_working_papers Chapman Digital Commons]<br />
<br />
== Spring 2020 ==<br />
<br />
The seminar talks are held in '''Keck Center for Science and Engineering, KC 370''' (Center St. Orange, CA 92866, intersection of Center St. And Sycamore St.), '''usually on Wednesday at 4 pm'''.<br />
Sometimes there will be a change of time or venue and the announcement will reflect this change.<br />
<br />
See [http://www.chapman.edu/about/maps-directions/index.aspx Maps<br />
and directions], Keck Center is Building 28 on the Campus Map [https://www.chapman.edu/about/_files/maps-and-directions/current-maps/campus-map.pdf <br />
Campus map]<br />
<br />
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<br />
=== Friday, Feb 21st, 2020, noon - 1 pm in Keck 370, refreshments at 11:45 am (same room) ===<br />
<br />
==== ''Speaker:'' '''Christian Williams, University of California at Riverside''' ====<br />
<br />
''Title:'' '''Predicate Calculus for Algebraic Theories'''<br />
<br />
''Abstract:'' There is a notion of predicate for algebraic theories, which admits a calculus of both logical and algebraic operations. We thereby extend equational logic by first-order logic, and provide a natural type theory for algebraic structures.<br />
<br />
We demonstrate the idea with the theory of monoids, and derive the example predicate "prime". This and many algebraic examples are only useful when they are mapped from a theory into actual models. There is much to be done in this direction. However, the driving motivation of this work is the application to programming languages: we focus on applying the idea to a more general notion of theory with variable binding.<br />
<br />
The construction is given in the topos of presheaves on a theory T: a "predicate" is a sieve on an object t of T, which corresponds to a subfunctor of the representable T(-,t). For each type t, these predicates form a Heyting algebra, providing the constructors of intuitionistic logic. The operations of T can be lifted to act on predicates, and we construct a model Pred(T): T -->HeyAlg. The correspondence between the operations of T and those in the image of Pred(T) gives that the former are "polymorphic" with respect to the types of the latter. This process can be understood as providing the theory T with a polymorphic type system.<br />
<br />
The original motivation of this work is a logic for concurrency known as Namespace Logic. This applies to the reflective higher-order pi calculus, which is the language of the distributed computing platform RChain. We demonstrate the above framework by constructing namespace logic. This gives a glimpse into a large field of potential application.<br />
<br />
[http://math.chapman.edu/~jipsen/seminarposters/Christian_Williams_pcat_2020-02-21.pdf Slides from the talk]<br />
<br />
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=== Wednesday, Feb 19th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Simon Cho, University of Michigan''' ====<br />
''Title:'' '''A categorical perspective on persistent and magnitude homology'''<br />
<br />
''Abstract:'' We define and explain both persistent homology and magnitude homology, and their respective roles in applications (in both pure and applied settings). We will exhibit how both arise as a "singular complex" of a metric space in essentially the same way, but for different values of a parameter.<br />
<br />
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=== Wednesday, Feb 12th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Stephon Alexander, Brown University, Rhode Island''' ====<br />
''Title:'' '''The Quantum Cosmological Constant'''<br />
<br />
''Abstract:'' The mysteries surrounding the Cosmological Constant presides at the interface of quantum mechanics and gravity. In this seminar,<br />
I will provide a pedagogical discussion of the many faces of the cosmological constant problem and discuss some current research that<br />
paves new directions that invites us to rethink the quantum nature of vacuum energy.<br />
<br />
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<br />
=== Tuesday, Jan 14th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Pedram Roushan, Google Inc., Santa Barbara, CA''' ====<br />
''Title:'' '''Quantum supremacy using a programmable superconducting processor'''<br />
<br />
''Abstract:'' The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor1. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 2^53 (about 10^16). Measurements from repeated experiments sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 seconds to sample one instance of a quantum circuit a million times—our benchmarks currently indicate that the equivalent task for a state-of-the-art classical supercomputer would take approximately 10,000 years. This dramatic increase in speed compared to all known classical algorithms is an experimental realization of quantum supremacy for this specific computational task, heralding a much-anticipated computing paradigm. If time permits, I will present some of our more recent measurements. <br />
<br />
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<br />
== Fall 2019 ==<br />
<br />
The seminar talks are held in '''Keck Center for Science and Engineering, KC 370''' (Center St. Orange, CA 92866, intersection of Center St. And Sycamore St.), '''usually on Wednesday at 4 pm'''.<br />
Sometimes there will be a change of time or venue and the announcement will reflect this change.<br />
<br />
See [http://www.chapman.edu/about/maps-directions/index.aspx Maps<br />
and directions], Keck Center is Building 28 on the Campus Map [https://www.chapman.edu/about/_files/maps-and-directions/current-maps/campus-map.pdf <br />
Campus map]<br />
<br />
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<br />
=== Thursday, Dec 12th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Alí Guzmán Adán, Universiteit Gent, Belgium''' ====<br />
''Title:'' '''Pizzetti and Cauchy formulae for higher dimensional surfaces: a<br />
distributional approach'''<br />
<br />
''Abstract:'' In this talk, we study Pizzetti-type formulas for Stiefel<br />
manifolds and Cauchy-type formulas for the tangential Dirac operator<br />
from a distributional perspective. First, we illustrate a general<br />
distributional method for integration over manifolds in R^m defined by<br />
means of k equations. We apply this method to derive an alternative<br />
proof of the Pizzetti formulae for the real Stiefel manifolds<br />
SO(m)/SO(m-k). Besides, a distributional interpretation of invariant<br />
oriented integration is provided. In particular, we obtain a<br />
distributional Cauchy theorem for the tangential Dirac operator on an<br />
embedded (m-k)-dimensional smooth surface.<br />
<br />
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<br />
=== Wednesday, Dec 11th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Arjendu K Pattanayak, Physics and Astronomy, Carleton College, Northfield, Minnesota''' ====<br />
''Title:'' '''Quantum entanglement and tunneling oscillations in a (few) many-body nonlinear spin system'''<br />
<br />
''Abstract:'' Quantum tunnelling permits recoherence or refocusing in real or phase space after the initial quantum state has seemingly delocalized, exhibiting so-called classically forbidden dynamics. For a nonlinearly interacting many-body spin system this interim state can be an entangled state. We report on recent results from investigations into this phenomenon for initially spin coherent pure states in the paradigmatic kicked top (vale Haake) system. This has a mixed regualar and chaotic phase space in the classical limit and exhibits the entanglement tunneling described above, including coherent dynamics between phase-space stability islands; here the interim state is maximally entangled. We map the dependence on various parameters including nonlinear spin and number of spins involved (focusing mostly on the remarkable special case N=4) using a metric that attempts to quantify the quality and rate of tunnelling. The calculations of tunneling rates using eigenvalues and eigenstates of the time evolution operator as a function of initial condition compared to classical space structures demonstrates several nontrivial ways in which quantum behavior transitions to classical as the size of the system grows.<br />
<br />
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=== Wednesday, Dec 4th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===<br />
<br />
==== ''Speaker:'' '''Raphael Drumond, Universidade Federal de Minas Gerais, Brazil''' ====<br />
''Title:'' '''The basics of Quantum Darwinism (and its relationship with non-Markovianity)'''<br />
<br />
''Abstract:'' Some aspects of physical systems described by quantum <br />
mechanics, most notably the possibility of violating a Bell inequality, <br />
suggests (to some) or unavoidably implies (to others) that certain <br />
properties of microscopic systems, like the precise values of position <br />
and momentum of a fundamental particle, do not have an objective <br />
reality. This strongly contrasts with the objectivity of properties of <br />
everyday macroscopic systems like the (rough estimate of) position and <br />
momentum of a baseball. Now, how can this objectivity of the <br />
macroscopic world emerge from a theory where, apparently, not all <br />
aspects of physical systems are objective? The notion of quantum <br />
Darwinism, put forward and popularized by Wojciech Zurek, is a path in <br />
that direction. In this talk I will discuss the main ideas behind <br />
quantum Darwinism, explore it in some simple models, and briefly discuss <br />
its relationship (or the lack of it) with the notion of non-Markovianity <br />
of quantum dynamical systems.<br />
<br />
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<br />
=== Thursday, Nov 21th, 2019, 12:30 - 1:30 pm in Keck 370, refreshments from 12:15 (same room) ===<br />
<br />
==== ''Speaker:'' '''Sandu Popescu, University of Bristol, UK''' ====<br />
''Title:'' '''Exploring the limits of no-backward-in-time signaling'''<br />
<br />
''Abstract:'' One of the most routine observations that we make about our world is that we cannot signal backwards in time. So ubiquitous is this understanding that it is often taken as one of the basic laws of Nature. At first glance, this remark seems straightforward. However, as I will show, in probabilistic theories such as quantum mechanics, the consequences of such an assertion are far more involved. In fact, we will see that there is a surprising amount of liberty: some theories even allow the future to affect the past, nevertheless without signaling backwards in time.<br />
<br />
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<br />
=== Friday, Nov 8th, 2019, 3 - 4 pm in Keck 171, refreshments from 2:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Fredrik Dahlqvist, University College London, UK''' ====<br />
<br />
''Title:'' '''A probabilistic approach to floating point arithmetic'''<br />
<br />
''Abstract:'' Finite-precision floating point arithmetic introduces rounding errors which are traditionally bounded using a worst-case analysis. However, worst-case analysis might be overly conservative because worst-case errors can be extremely rare events in practice. Here we develop a probabilistic model of rounding errors with which it becomes possible to quantify the likelihood that the rounding error of an algorithm lies within a given interval. <br />
<br />
Given an input distribution, the model requires the distribution of rounding errors. We show how to exactly compute this distribution for low precision arithmetic. For high precision arithmetic we derive a simple but surprisingly useful approximation. The model is then entirely compositional: given a numerical program written in a simple imperative programing language we can recursively compute the distribution of rounding errors at each step and propagate it through each program instruction. This is done by applying a formalism originaly developed by Kozen to understand the semantics of probabilistic programs, for example how probability distributions gets transformed by assignments or "if then else" statements.<br />
<br />
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<br />
=== Wednesday, Nov 6th, 2019, 4 - 5 pm in Keck 370, refreshments from 3:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Jacques Pienaar, International Institute of Physics in Natal, Brazil''' ====<br />
<br />
''Title:'' '''The new question in quantum foundations: what is causality?'''<br />
<br />
''Abstract:'' Work in quantum foundations has tended to concentrate on Bell's Theorem, <br />
but recently a particular aspect of that theorem has taken on a life of <br />
its own: the question of what "causality" means in quantum mechanics, <br />
and how to model it. This movement has been driven in large part by <br />
recent advances in causal modeling in the statistical and Artificial <br />
Intelligence communities, which have had a heavy influence on quantum <br />
causal modeling. These "classical" approaches tend to define causality <br />
as a probabilistic and action-centered concept, which fits well with <br />
modern information-theoretic treatments of quantum mechanics. However, <br />
the classical approaches also tend to emphasize notions of underlying <br />
determinism and objective mechanisms that do not sit so well in the <br />
quantum context. In this talk I will step back from most of the <br />
technical jargon and try to get to the heart of some of the conceptual <br />
issues involved in "quantizing" the concept of causality, critically <br />
reviewing some key findings, pointing out potential inconsistencies and <br />
outlining possible directions for further inquiry into this fascinating <br />
problem.<br />
<br />
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<br />
=== Friday, October 18th, 2019, 12 - 1 pm in Keck 370, refreshments from 11:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Prof. Lev Vaidman, Alex Maguy-Glass Chair in Physics of Complex Systems, Tel Aviv University, Israel''' ====<br />
<br />
''Title:'' '''The past of a quantum particle'''<br />
<br />
''Abstract:'' Textbooks of quantum mechanics lack the concept of the past of quantum systems. Few years ago I proposed to define the past of a quantum particle according to the trace it leaves. While in many cases this definition provides a reasonable description, for a nested Mach-Zehnder interferometer it leads to a picture seemingly contradicting common sense: the particle leaves a trace in a place through which it could not pass. I will discuss recent theoretical and experimental studies of this controversial issue.<br />
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=== Friday, October 11th, 2019, 1 - 2 pm in Keck 370, refreshments from 12:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Prof. Thomas Curtright, University of Miami''' ====<br />
<br />
''Title:'' '''Massive Dual Gravity Revisited'''<br />
<br />
''Abstract:'' I will describe a highly speculative model of gravity as a massive,<br />
pure spin 2 field, which is "dual" to the usual description in terms of<br />
a spacetime metric tensor.<br />
<br />
In the dual description, for weak fields, the metric emerges as the<br />
field strength of an underlying fundamental field. More generally, if<br />
the gravitational field is not weak, the metric emerges as a nonlinear<br />
mixture involving the energy momentum tensor.<br />
<br />
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<br />
=== Wednesday, October 9th, 2019, 4 - 5 pm in Keck 370, refreshments from 3:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Alain Hénaut, Institut de Mathématiques de Bordeaux, Université de Bordeaux, France''' ====<br />
<br />
''Title:'' '''On planar web geometry'''<br />
<br />
''Abstract:'' Web geometry deals with foliations in general position. In the planar case and the complex setting, a $d$-web is given by the generic family of integral curves of an analytic or an algebraic differential equation $F(x,y,y')=0$ with $y'$-degree $d$. Invariants of these configurations as abelian relations (related to Abel's addition theorem), Lie symmetries or Godbillon-Vey sequences are investigated. This viewpoint enlarges the qualitative study of differential equations and their moduli. In the nonsingular case and through the singularities, Cartan-Spencer and meromorphic connections methods will be used. Basic examples will be given from different domains including classic algebraic geometry and WDVV-equations. Standard results and open problems will be mentioned. Illustration of the interplay between differential and algebraic geometry, new results will be presented. <br />
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<br />
=== Thursday, September 5th, 2019, 4 - 5 pm in Keck 171, refreshments from 3:45 (same room) ===<br />
<br />
==== ''Speaker:'' '''Nicole Yunger Halpern, Harvard-Smithsonian ITAMP (Institute for Theoretical Atomic, Molecular, and Optical Physics) Harvard University Department of Physics''' ====<br />
<br />
''Title:'' '''Entropic uncertainty relations for quantum-information scrambling'''<br />
<br />
''Abstract:'' How violently do two quantum operators disagree? Different subfields of physics feature different notions of incompatibility: (i) In quantum information theory, uncertainty relations are cast in terms of entropies. These entropic uncertainty relations constrain measurement outcomes. (ii) Condensed matter and high-energy physics feature interacting quantum many-body systems, such as spin chains. A local perturbation, such as a Pauli operator on one side of a chain, spreads through many-body entanglement. The perturbation comes to overlap, and to disagree, with probes localized on the opposite side of the system. This disagreement signals that quantum information about the perturbation has scrambled, or become hidden in highly nonlocal correlations. I will unite these two notions of quantum operator disagreement, presenting an entropic uncertainty relation for quantum-information scrambling. The entropies are of distributions over weak and strong measurements’ possible outcomes. The uncertainty bound strengthens when a spin chain scrambles in numerical simulations. Hence the subfields—quantum information, condensed matter, and high-energy physics—can agree about when quantum operations disagree. Our relation can be tested experimentally with superconducting qubits, trapped ions, and quantum dots.<br />
<br />
NYH, Bartolotta, and Pollack, Comms. Phys. 2, 92 (2019). https://www.nature.com/articles/s42005-019-0179-8<br />
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=== Monday, August 26, 2019, 7 - 8:30 pm, in Argyros Forum, Room 209 A&B, networking from 6:15 to 7pm (same room) ===<br />
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==== ''Speaker:'' '''Frederick Eberhardt, Professor of Philosophy in the Division of the Humanities and Social Sciences at the California Institute of Technology''' ====<br />
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''Title:'' '''Computing Causal Relations at Scale or Causality: From Aristotle through Computing to Zebrafish'''<br />
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''Abstract:'' What causes what? How do we untangle the “why” behind processes that regulate the brain, the climate or the economy? If “Correlation does not imply causation" is the standard mantra in science, how can we ever discover causal relationships behind the data? Will it ever be possible for intelligent AI to make its own deductions and predictions? In recent years researchers have developed mathematical techniques that give us the power to infer the underlying “why” behind scientific data. What’s more, we’ve learned that we can discover these causes without performing experiments. Starting with a little practical example with lightbulbs that can be worked out by hand we will see how the problem scales as the number of variables increases. To compute the neural connections in a zebrafish brain, high performance computing is essential.<br />
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''Bio:'' Frederick Eberhardt is Professor of Philosophy in the Division of the Humanities and Social Sciences at the California Institute of Technology. Before coming to Caltech he was Assistant Professor in the Philosophy-Neuroscience-Psychology (PNP) program and the Department of Philosophy at Washington University in St. Louis and a postdoc at the Institute of Cognitive and Brain Sciences at the University of California, Berkeley. As an undergraduate he attended the London School of Economics for a Bachelor in Philosophy & Mathematics. He received his PhD in philosophy from Carnegie Mellon University, where he also completed a Masters in Machine Learning.<br />
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His research interests lie at the intersection of philosophy of science, machine learning and statistics. He is particularly interested in the development of methods for causal discovery from statistical data.<br />
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== Previous Seminar talks ==<br />
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* [[MPC Seminar 2019]]<br />
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* [[MPC Seminar 2018]]<br />
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* [[MathCS Seminar 2017]]<br />
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* [[MathCS Seminar 2016]]<br />
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* [[MathCS Seminar 2015]]<br />
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* [[MathCS Seminar 2014]]<br />
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* [[MathCS Seminar 2013]]<br />
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* [[MathCS Seminar 2012]]<br />
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* [[MathCS Seminar 2011]]<br />
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* [[MathCS Seminar 2010]]<br />
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* [[MathCS Seminar 2009]]<br />
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* [[MathCS Seminar 2008]]<br />
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* [[MathCS Seminar 2007]]<br />
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* [[MathCS Seminar 2006]]<br />
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* [[MathCS Seminar 2005]]<br />
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* [[MathCS Seminar 2004]]<br />
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* [[MathCS Seminar 2003]]<br />
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* [[MathCS Seminar 2002]]</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=Main_Page&diff=3Main Page2021-02-22T18:26:05Z<p>Jipsen: </p>
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<div><big>'''This is the main page of the Chapman University Math Wiki'''</big><br />
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== Useful Links ==<br />
[http://math.chapman.edu/ Faculty of Mathematics]<br />
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The following web pages are dedicated to our Math-Physics-Computation (MPC) Seminar and other resources.<br />
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* Our [[MPC Seminar]]<br />
* [http://canvas.chapman.edu/ Canvas at Chapman University]<br />
* MathSciNet https://mathscinet-ams-org.libproxy.chapman.edu/<br />
* zbMATH Open https://www.zbmath.org/<br />
* ArXiv Math https://arxiv.org/archive/math<br />
* Chapman Library https://www1.chapman.edu/library/<br />
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* American Mathematical Society https://www.ams.org/home/page<br />
* Mathematical Association of America https://www.maa.org/<br />
* Association of Computing Machinery https://www.acm.org/<br />
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* Mathematics Genealogy Project https://genealogy.math.ndsu.nodak.edu/<br />
* The MacTutor History of Mathematics Archive https://www-history.mcs.st-and.ac.uk/<br />
* Encyclopedia of Integer Sequences https://www.research.att.com/~njas/sequences/<br />
* [https://math.chapman.edu/~jipsen/structures Mathematical Structures Homepage]<br />
* CoCalc: A powerful online computer algebra system https://cocalc.com<br />
* Colab: A free online Jupyter notebook https://colab.research.google.com/<br />
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* Wikipedia [http://en.wikipedia.org/wiki/Mathematics Mathematics], [http://en.wikipedia.org/wiki/Computer_science Computer Science], [http://en.wikipedia.org/wiki/Physics Physics], [http://en.wikipedia.org/wiki/Computational_science Computational Science]<br />
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* PlanetMath http://planetmath.org/<br />
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* Wolfram Alpha http://www.wolframalpha.com</div>Jipsenhttps://mathtest.chapman.edu/mathcs/index.php?title=Main_Page&diff=2Main Page2021-02-22T18:23:30Z<p>Jipsen: </p>
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<div><big>'''This is the main page of the Chapman University Math Wiki'''</big><br />
<br />
== Useful Links ==<br />
[http://math.chapman.edu/ Faculty of Mathematics]<br />
<br />
[http://www1.chapman.edu/SCS/CS/ School of Computational Science]<br />
<br />
The following web pages are dedicated to our Math Physics Computation Seminar and other resources.<br />
<br />
* Our [[MPC Seminar]]<br />
* [http://canvas.chapman.edu/ Canvas at Chapman University]<br />
* MathSciNet https://mathscinet-ams-org.libproxy.chapman.edu/<br />
* zbMATH Open https://www.zbmath.org/<br />
* ArXiv Math https://arxiv.org/archive/math<br />
* Chapman Library https://www1.chapman.edu/library/<br />
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* American Mathematical Society https://www.ams.org/home/page<br />
* Mathematical Association of America https://www.maa.org/<br />
* Association of Computing Machinery https://www.acm.org/<br />
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* Mathematics Genealogy Project https://genealogy.math.ndsu.nodak.edu/<br />
* The MacTutor History of Mathematics Archive https://www-history.mcs.st-and.ac.uk/<br />
* Encyclopedia of Integer Sequences https://www.research.att.com/~njas/sequences/<br />
* [https://math.chapman.edu/~jipsen/structures Mathematical Structures Homepage]<br />
* CoCalc: A powerful online computer algebra system https://cocalc.com<br />
* Colab: A free online Jupyter notebook https://colab.research.google.com/<br />
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* Wikipedia [http://en.wikipedia.org/wiki/Mathematics Mathematics], [http://en.wikipedia.org/wiki/Computer_science Computer Science], [http://en.wikipedia.org/wiki/Physics Physics], [http://en.wikipedia.org/wiki/Computational_science Computational Science]<br />
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* PlanetMath http://planetmath.org/<br />
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* Wolfram Alpha http://www.wolframalpha.com</div>Jipsen