# MPC Seminar 2019

## 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 St.), **usually on Wednesday at 4 pm**.
Sometimes there will be a change of time or venue and the announcement will reflect this change.

See [http://www.chapman.edu/about/maps-directions/index.aspx Maps 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 Campus map]

### Thursday, May 16, 2019 at 3 pm, in Keck 370, tea and cookies at 2:40pm (same room)

#### *Speaker:* **Dr. Purbita Jana, The Institute of Mathematical Sciences, Chennai, India**

*Title:* **Intuitionistic topological systems and their connections with Heyting algebra and Gödel algebra**

*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).

### Tuesday, April 16, 2019 at 5 pm, in Keck 370, tea and cookies at 3:40pm (same room)

#### *Speaker:* **Dr. Michele Piazzai, University of Amsterdam, Netherlands**

*Title:* **The Ecology of Ideas: Computational Evidence of Self-Organization**

*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.

### Thursday, April 11, 2019 at 4 pm, in Keck 370, tea and cookies at 3:40pm (same room)

#### *Speaker:* **Dr. Michele Piazzai, University of Amsterdam, Netherlands**

*Title:* **The Ecology of Ideas: Empirical Evidence of Evolutionary Pressure**

*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.

### Thursday, March 28, 2019 at 5 pm, in Keck 171, tea and cookies at 4:40pm (same room)

#### *Speaker:* **Prof. Giovanni Sambin, University of Padova, Italy**

*Title:* **Half way to Grothendieck's aim (embedding of pointwise topology into pointfree topology)**

*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.
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.
This embedding does not look possible without exploiting the presence of the new (intrinsically existential) notion of positivity relation.
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.

### Wednesday, March 13, 2019 at 4 pm, in Keck 171, tea and cookies at 3:45pm in Keck 370

#### *Speaker:* **Dr. Matt Pusey, University of Oxford**

*Title:* **Anomalous weak values and contextuality: robustness and imaginary**
parts

*Abstract:* I will discuss extensions to my previous work linking anomalous weak
values with contextuality. In particular, I will show that using
transformation noncontextuality obviates the experimentally
problematic requirement that the post-selection is projective. I will
also discuss the status of the imaginary part of weak values. My talk
will be based on joint work with Ravi Kunjwal and Matteo Lostaglio:
https://arxiv.org/abs/1812.06940

### Wednesday, February 27, 2019 at 4 pm, in Keck 171, tea and cookies at 3:45pm in Keck 370

#### *Speaker:* **Prof. Christos Tzounis, California State Polytechnic University, Pomona**

*Title:* **Metric of an Evaporating Black Hole**

*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.

### Wednesday, February 13, 2019 at 4 pm, in Keck 171, tea and cookies at 3:45pm in Keck 370

#### *Speaker:* **Prof. Peter Rakitzis, Institute of Electronic Structure and Laser, Heraklion, Greece**

*Title:* **Ultrahigh-Density Spin-Polarized H and D Atoms Observed via Magnetization Quantum Beats**

*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.

### Tuesday, February 5 -- Saturday, February 9, 2019 in Keck 370

#### **11th Annual Chapman University CECAT Workshop on Pointfree Mathematics**

TUESDAY, February 5th:

1:00 - 2:00pm **M. Andrew Moshier**, *Chapman University*, Weakening relations

THURSDAY, February 7th:

10:30 - 11:30am: **Peter Jipsen**, *Chapman University*, Involutive residuated lattices and relation algebras

11:30 - 12:30pm: **Sara Vannucci**, *University of Salerno*, Semiring and Semimodule Issues in Residuated Lattices

1:00 - 2:15pm: **Rick Ball**, *University of Denver*, Pointfree Integration

2:15 - 3:15pm: **Anna Laura Suarez**, *University of Birmingham*, D-frames and frame coproducts

3:30 - 4.30pm: **Alex Kurz**, *Chapman University*, On the duality theory of weakening relations

FRIDAY, February 8th

10:30 - 11:30am: **Ales Pultr**, *Charles University*, Strong Hausdorff properties of frames

11:30 - 12:30pm: **Diego Valota**, *University of Milan*, Computing Spectra via Dualities in the MTL hierarchy

2:00 - 3:00pm: **Olim Tuyt**, *University of Bern*, Algebraic finite model property of a modal Gödel logic

3:00 - 4:15pm: **Rick Ball**, *University of Denver*, Pointfree Integration, continued

SATURDAY, February 9th

1:00 - 5:00pm: Discussion session