# MPC Seminar

This is the homepage of the Chapman University **Mathematics, Physics, and Computation Seminars**
(MPC Seminar)

*Seminar Organizers:* Roman Buniy and Peter Jipsen

## Spring 2021

The MPC seminar is held via Zoom for now. The Zoom address will be sent in the email announcements.

### Monday, May 3rd, 2021, 1 - 2 pm on Zoom

*Speaker:* **Simon Henry, University of Ottawa**

*Title:* **Localic C*-algebras and the Geometric Bohr topos**

*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.

*Link to paper:* [1]

### Thursday, Jan 21st, 2021, 4 - 5 pm on Zoom

*Speaker:* **Mike Campbell, Eureka (SAP), joint work with Vernon Smith (Chapman University)**

*Title:* **An Elementary Humanomics Approach to Boundedly Rational Quadratic Models**

*Video of talk:* YouTube *Slides:* pdf

*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.

*Link to paper:* Chapman Digital Commons

## Spring 2020

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**.
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]

### Friday, Feb 21st, 2020, noon - 1 pm in Keck 370, refreshments at 11:45 am (same room)

*Speaker:* **Christian Williams, University of California at Riverside**

*Title:* **Predicate Calculus for Algebraic Theories**

*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.

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.

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.

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.

### Wednesday, Feb 19th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room)

*Speaker:* **Simon Cho, University of Michigan**

*Title:* **A categorical perspective on persistent and magnitude homology**

*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.

### Wednesday, Feb 12th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room)

*Speaker:* **Stephon Alexander, Brown University, Rhode Island**

*Title:* **The Quantum Cosmological Constant**

*Abstract:* The mysteries surrounding the Cosmological Constant presides at the interface of quantum mechanics and gravity. In this seminar,
I will provide a pedagogical discussion of the many faces of the cosmological constant problem and discuss some current research that
paves new directions that invites us to rethink the quantum nature of vacuum energy.

### Tuesday, Jan 14th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room)

*Speaker:* **Pedram Roushan, Google Inc., Santa Barbara, CA**

*Title:* **Quantum supremacy using a programmable superconducting processor**

*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.

## Fall 2019

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**.
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, Dec 12th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room)

*Speaker:* **Alí Guzmán Adán, Universiteit Gent, Belgium**

*Title:* **Pizzetti and Cauchy formulae for higher dimensional surfaces: a**
distributional approach

*Abstract:* In this talk, we study Pizzetti-type formulas for Stiefel
manifolds and Cauchy-type formulas for the tangential Dirac operator
from a distributional perspective. First, we illustrate a general
distributional method for integration over manifolds in R^m defined by
means of k equations. We apply this method to derive an alternative
proof of the Pizzetti formulae for the real Stiefel manifolds
SO(m)/SO(m-k). Besides, a distributional interpretation of invariant
oriented integration is provided. In particular, we obtain a
distributional Cauchy theorem for the tangential Dirac operator on an
embedded (m-k)-dimensional smooth surface.

### Wednesday, Dec 11th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room)

*Speaker:* **Arjendu K Pattanayak, Physics and Astronomy, Carleton College, Northfield, Minnesota**

*Title:* **Quantum entanglement and tunneling oscillations in a (few) many-body nonlinear spin system**

*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.

### Wednesday, Dec 4th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room)

*Speaker:* **Raphael Drumond, Universidade Federal de Minas Gerais, Brazil**

*Title:* **The basics of Quantum Darwinism (and its relationship with non-Markovianity)**

*Abstract:* Some aspects of physical systems described by quantum
mechanics, most notably the possibility of violating a Bell inequality,
suggests (to some) or unavoidably implies (to others) that certain
properties of microscopic systems, like the precise values of position
and momentum of a fundamental particle, do not have an objective
reality. This strongly contrasts with the objectivity of properties of
everyday macroscopic systems like the (rough estimate of) position and
momentum of a baseball. Now, how can this objectivity of the
macroscopic world emerge from a theory where, apparently, not all
aspects of physical systems are objective? The notion of quantum
Darwinism, put forward and popularized by Wojciech Zurek, is a path in
that direction. In this talk I will discuss the main ideas behind
quantum Darwinism, explore it in some simple models, and briefly discuss
its relationship (or the lack of it) with the notion of non-Markovianity
of quantum dynamical systems.

### Thursday, Nov 21th, 2019, 12:30 - 1:30 pm in Keck 370, refreshments from 12:15 (same room)

*Speaker:* **Sandu Popescu, University of Bristol, UK**

*Title:* **Exploring the limits of no-backward-in-time signaling**

*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.

### Friday, Nov 8th, 2019, 3 - 4 pm in Keck 171, refreshments from 2:45 (same room)

*Speaker:* **Fredrik Dahlqvist, University College London, UK**

*Title:* **A probabilistic approach to floating point arithmetic**

*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.

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.

### Wednesday, Nov 6th, 2019, 4 - 5 pm in Keck 370, refreshments from 3:45 (same room)

*Speaker:* **Jacques Pienaar, International Institute of Physics in Natal, Brazil**

*Title:* **The new question in quantum foundations: what is causality?**

*Abstract:* Work in quantum foundations has tended to concentrate on Bell's Theorem,
but recently a particular aspect of that theorem has taken on a life of
its own: the question of what "causality" means in quantum mechanics,
and how to model it. This movement has been driven in large part by
recent advances in causal modeling in the statistical and Artificial
Intelligence communities, which have had a heavy influence on quantum
causal modeling. These "classical" approaches tend to define causality
as a probabilistic and action-centered concept, which fits well with
modern information-theoretic treatments of quantum mechanics. However,
the classical approaches also tend to emphasize notions of underlying
determinism and objective mechanisms that do not sit so well in the
quantum context. In this talk I will step back from most of the
technical jargon and try to get to the heart of some of the conceptual
issues involved in "quantizing" the concept of causality, critically
reviewing some key findings, pointing out potential inconsistencies and
outlining possible directions for further inquiry into this fascinating
problem.

### Friday, October 18th, 2019, 12 - 1 pm in Keck 370, refreshments from 11:45 (same room)

*Speaker:* **Prof. Lev Vaidman, Alex Maguy-Glass Chair in Physics of Complex Systems, Tel Aviv University, Israel**

*Title:* **The past of a quantum particle**

*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.

### Friday, October 11th, 2019, 1 - 2 pm in Keck 370, refreshments from 12:45 (same room)

*Speaker:* **Prof. Thomas Curtright, University of Miami**

*Title:* **Massive Dual Gravity Revisited**

*Abstract:* I will describe a highly speculative model of gravity as a massive,
pure spin 2 field, which is "dual" to the usual description in terms of
a spacetime metric tensor.

In the dual description, for weak fields, the metric emerges as the field strength of an underlying fundamental field. More generally, if the gravitational field is not weak, the metric emerges as a nonlinear mixture involving the energy momentum tensor.

### Wednesday, October 9th, 2019, 4 - 5 pm in Keck 370, refreshments from 3:45 (same room)

*Speaker:* **Alain Hénaut, Institut de Mathématiques de Bordeaux, Université de Bordeaux, France**

*Title:* **On planar web geometry**

*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.

### Thursday, September 5th, 2019, 4 - 5 pm in Keck 171, refreshments from 3:45 (same room)

*Speaker:* **Nicole Yunger Halpern, Harvard-Smithsonian ITAMP (Institute for Theoretical Atomic, Molecular, and Optical Physics) Harvard University Department of Physics**

*Title:* **Entropic uncertainty relations for quantum-information scrambling**

*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.

NYH, Bartolotta, and Pollack, Comms. Phys. 2, 92 (2019). https://www.nature.com/articles/s42005-019-0179-8

### Monday, August 26, 2019, 7 - 8:30 pm, in Argyros Forum, Room 209 A&B, networking from 6:15 to 7pm (same room)

*Speaker:* **Frederick Eberhardt, Professor of Philosophy in the Division of the Humanities and Social Sciences at the California Institute of Technology**

*Title:* **Computing Causal Relations at Scale or Causality: From Aristotle through Computing to Zebrafish**

*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.

*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.

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.