# 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 2023

The MPC seminar is held in-person in the **Keck Center of Science and Engineering, Room 372** (unless a speaker prefers to hold the talk over Zoom). The date and time are included in the announcements below.

### Monday, March 6, 2023, 12:30 - 1:30 pm in Keck 372

*Speaker:* **Papiya Battacharjee, Florida Atlantic University**

*Title:* **Martinez Frames and d-Elements**

*Abstract:* Given an algebraic frame with FIP (M-frame), we can study the d-operator on such frames. The d-operator is a special type of nucleus on an M-frame which generates the frame of all d-elements, dL. We call an M-frame a Martinez frame if dL=L. During this presentation we will discuss d-elements of an M-frame and give several characterizations of Martinez frames. In the last half of the presentation we will discuss Max(dL), a subspace of Spec(L) consisting of the maximal d-elements of L.

### Thursday, February 23, 2023, 4:00 - 5:00 pm in Keck 372

*Speaker:* **Ahmed Sebbar, Chapman University**

*Title:* **Graph Theory II, The adjacency matrix and some of its properties**

*Abstract:* The adjacency matrix is important in Graph Theory and in Computer Science. We study the properties of its powers and give an interpretation of their coefficients. This prepares us to introduce Ihara's zeta function of a finite graph and its arithmetic.

## Fall 2022

### Friday, December 9, 2022, 3:10 - 4:10 pm in Keck 372

*Speaker:* **Ahmed Sebbar, Chapman University**

*Title:* **Elementary Graph Theory and Elementary Number Theory**

*Abstract:* We give an introduction to graph theory, adjacency matrices and interpretation of their powers. We define the Ihara Zeta function and compute a few examples. We will briefly discuss Ramanujan graphs.

## Fall 2021

### Thursday, September 23, 2021, 12:30 - 1:30 pm in AF 209C

*Speaker:* **Lev Vaidman, Tel Aviv University**

*Title:* **Counterfactual communication**

*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.

## Spring 2021

### 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:* arxiv.org/pdf/1502.01896.pdf

### 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.