# MathCS Seminar

This is the homepage of the Chapman University Mathematics and Computational Science seminar

Seminar Organizers: Cyril Rakovski and Mihaela Vajiac

## Spring 2014

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 Maps and directions, Von Neumann Hall is Building 38 on the Campus map

## Previous Talks and Workshops

### Wednesday, May 14, 2014 from noon to 12:50 pm in VN 116

#### Speaker: Dr. Roman Buniy, Chapman University

Title: Generalized helicity and Beltrami fields

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 local constraint $\epsilon^{\mu\nu\alpha\beta}{F_{\mu\nu}F_{\alpha\beta}}=0$ satisfies the covariant non-abelian Beltrami equation.

### Thursday, May 8, 2014 from 4pm to 5pm in Von Neumann Hall

#### Speaker: Dr. Hendrik De Bie, Assistant-professor, Clifford Research Group, Ghent University

Title: Convolutions for the quaternion Fourier transform with applications in image processing

Abstract: In this lecture I will explain how a quaternion Fourier transform may be defined, an how a suitable convolution product can be associated with it.I will subsequently discuss an application in color image processing, namely a color edge detector. If time allows, I will also show how some of these results may be generalized to higher dimensions using Clifford algebras.

### Thursday, April 24, 2014 from 4pm to 5pm in Von Neumann Hall

#### Speakers: Ryan Burns, Isaac Lien, Scott Lien, David Tyler

Title: GrandPAD: Finally technology so easy that it can be used by a people ages 75 to 105.

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. 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). Come and learn about the technology we have used to build GrandPAD and see the product in action. GrandPAD -- Simply Connected

### Thursday, April 17, 2014 from 4pm to 5pm in Von Neumann Hall

#### Speaker: Professor Andrew Moshier, Chapman University

Title: String diagrams for categories of posets

Abstract: String diagrams, e.g., for braiding and symmetric monoidal categories, have proven useful in Physics and Theoretical Computer Science, thanks to coherence theorems that tell us that diagrams equivalent under suitable topological invariants denote equal morphisms. In this talk, we extend a similar courtesy to categories of partially ordered sets by adding an order on diagrams and allowing for topologically "lossy" diagram rewrites. As an application, we characterize the objects in such categories that behave as semi-lattices, lattices and distributive lattices.

PDF copy of the abstract containing a diagram.

### Thursday, April 10, 2014 from 4pm to 5pm in Von Neumann Hall

#### Speaker: Dr. Ali Nayeri, Chapman University

Title: String Gas Cosmology and the Blue Tilt of the Primordial Gravitational Waves

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.

### Monday, April 7, 2014 at noon in Von Neumann Hall

#### Speaker: Dr. Cary Deck, University of Arkansas

Title: Behavior in Interconnected Strategic Contests

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.

### Wednesday, March 5, 2014 at noon in Von Neumann Hall

#### Speaker: Prof. Asen Dontchev, University of Michigan, Ann Arbor

Title: Inverse Function Theorems: Old and New

Abstract: The classical inverse/implicit function theorems revolves around solving an equation in terms of a parameter and tell us when the solution mapping associated with this equation is a differentiable function with respect to the parameter. In this talk we move into a much wider territory in replacing equation-solving by problems involving nonsmooth equations, as well as models of optimization, equilibrium, and control theory.

It turns out that if we put aside differentiability and focus on Lipschitz continuity only, or even more general metric regularity properties of mappings, we can cover a wider range of models and get estimates of the solution changes resulting from approximations of the model. As illustrations we will present implicit function theorems for inequalities and variational inequalities.

### Thursday, February 27, 2014 from 4pm to 5pm in Von Neumann Hall

#### Speaker: Professor Michael Campbell from CSUF

Title: Phase Transitions in Economic Models: Hot and Cold Market Equilibria in Bounded-Rational Potential Games

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.

## Fall 2013

### Thursday, Nov 21, 2013 from 2 pm to 4 pm in VN 116

#### Fifth Cal State University Fullerton and Chapman University Joint Mathematics Colloquium

Organizers: Bogdan Suceavă (CSUF) and Peter Jipsen (Chapman University)

Program

2:00 - 2:20 Fernando Quintino (Cal State Fullerton)
Interpolating Legendre Multiplier Sequences

2:20 - 2:40 Allie Smith and Louis Ehwerhemuepha (Chapman University)
A Novel Exact Test for Association for Small Sample Case-Control Studies

2:40 - 3:00 Nathan Robertson, Susan Deeb, Soeun Park, and Reina Galvez (Cal State Fullerton)
A Comparative Analysis of Three Clustering Techniques  with an Application to K6-11 Mathematics Achievement Data

3:00 - 3:20 Kevin Gomez (Cal State Fullerton)
A Ladder of Curvatures for Hypersurfaces in the Euclidean Ambient Space

3:20 - 3:40 Melissa Riddle (Cal State Fullerton)
A Pinching Theorem for Three-Dimensional Hypersurfaces in Euclidean Ambient Space

3:40 - 4:00 Kyle Lee (Chapman University)
Investigating Quantum Gravity through Causal Dynamical Triangulations

### Wednesday, Nov 13, 2013 at 12 noon in VN 116

#### Speaker: Daniele Struppa, Chapman University

Title: Propagation of superoscillations as solutions to the Cauchy problem for generalized Schrodinger equations

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.

### Wednesday, Oct 23, 2013 at 12 noon in VN 116

#### Speaker: Atanas Radenski, Chapman University

Title: MapReduce Streaming Algorithms for Laplace Relaxation on the Cloud

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.

### Wednesday, Sept 18, 2013 at 12 noon in VN 116

#### Speaker: Tadeusz Litak, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany

Title: Friends, Likes and Coalitions: Coalgebraic Predicate Logic in Action

Abstract: The talk is about a joint work with Dirk Pattinson, Katsuhiko Sano and Lutz Schröder. 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. However, I will assume no familiarity with coalgebras and coalgebraic logic. It is enough to know that the framework can cover such diverse structures as Kripke frames, neighbourhood frames, topological spaces, discrete Markov chains, conditional frames, multigraphs or game frames for coaliton logic/alternating time logics. As a taster, we will develop an apparatus to reason about activities and preferences in social networks. Then we will shortly discuss issues likes completeness, model theory and proof theory.