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Reaction-Diffusion Equations under Perturbations of the Domain (Professor Jose Arrieta, Universidad Complutense de Madrid, Spain)

Shanahan 3465, Harvey Mudd College 301 Platt Blvd., Claremont, CA, United States

We analyze the behavior of the asymptotic dynamics of dissipative reaction-diffusion equations with Neumann boundary conditions when the domain where the equation is posed undergoes certain perturbation. We will focus on the behavior of the stationary solutions, their local unstable manifolds and the attractors. We will consider "regular" perturbations of the domain, that is, perturbations […]

An Introduction to the Sato-Tate Conjecture (Edray Goins, Pomona College)

Millikan 2099, Pomona College 610 N. College Ave., Claremont, CA, United States

In 1846, Ernst Eduard Kummer conjectured a distribution of values of a cubic Gauss sum after computing a few values by hand.  This was forgotten about for nearly 100 years until John von Neumann and Herman Goldstine attempted to verify the conjecture as a way to test the new ENIAC machine in 1953.  They found […]

Modeling Mechanisms of Ovulatory (Dys)Function (Erica Graham, Bryn Mawr College)

Argue Auditorium, Pomona College 610 N. College Ave., Claremont, CA, United States

A normally functioning menstrual cycle requires significant crosstalk between hormones originating in ovarian and brain tissues. Reproductive hormone dysregulation may disrupt function and can lead to infertility, as occurs in the common endocrine disorder polycystic ovarian syndrome (PCOS). In this talk, I will discuss a mathematical model of the ovulatory cycle that accounts for mechanisms […]

GEMS Workshop: Knots and how to tell them apart (Professor Sam Nelson, Claremont McKenna College)

Shanahan 1480, Harvey Mudd College 301 Platt Blvd., Claremont, CA, United States

WHAT IS GEMS: The Gateway to Exploring Mathematics program (GEMS) is a series of workshops that helps excite the interests and curiosity of young students in mathematics and science GEMS meets once a month on a Saturday morning from 10:00 AM to 12:00 PM GEMS is designed to reach 8th, 9th and 10th grade students […]

Free

State Polytopes of Combinatorial Neural Codes (Rob Davis, HMC)

Millikan 2099, Pomona College 610 N. College Ave., Claremont, CA, United States

Combinatorial neural codes are 0/1 vectors that are used to model the co-firing patterns of a set of place cells in the brain. One wide-open problem in this area is to determine when a given code can be algorithmically drawn in the plane as a Venn diagram-like figure. A sufficient condition to do so is […]

Applications of Cayley Digraphs to Waring’s Problem and Sum-Product Formulas (Yesim Demiroglu, Harvey Mudd)

Argue Auditorium, Pomona College 610 N. College Ave., Claremont, CA, United States

Abstract: In this talk, we first present some elementary new proofs (using Cayley digraphs and spectral graph theory) for Waring's problem over finite fields, and explain how in the process of re-proving these results, we obtain an original result that provides an analogue of Sarkozy's theorem in the finite field setting (showing that any subset […]

Agent-Based and Continuous Models of Locust Hopper Bands: The Role of Intermittent Motion, Alignment, Attraction and Repulsion (Andrew J. Bernoff, HMC)

Emmy Noether Room, Millikan 1021, Pomona College 610 N. College Ave., Claremont, California

Locust swarms pose a major threat to agriculture, notably in northern Africa and the Middle East. In the early stages of aggregation, locusts form hopper bands. These are coordinated groups that march in columnar structures that are often kilometers long and may contain millions of individuals. We propose a model for the formation of locust […]

The Bateman—Horn Conjecture, Part I: heuristic derivation (Stephan Garcia, Pomona)

Millikan 2099, Pomona College 610 N. College Ave., Claremont, CA, United States

The Bateman—Horn Conjecture is a far-reaching statement about the distribution of the prime numbers.  It implies many known results, such as the Green—Tao theorem, and a variety of famous conjectures, such as the Twin Prime Conjecture.  In this expository talk, we start from basic principles and provide a heuristic argument in favor of the conjecture. […]

Great Expectations (Matthew Junge, Duke Univ.)

Argue Auditorium, Pomona College 610 N. College Ave., Claremont, CA, United States

The mean of a random quantity is supposed to confirm our expectations. What happens when it defies them? We will look at a few famous expected values; some old, some new, all great.

Isometric Circle Actions (Catherline Searle, Wichita State)

Argue Auditorium, Pomona College 610 N. College Ave., Claremont, CA, United States

I will begin by describing a number of important examples of isometric actions of circles in Euclidean space and their restrictions to subspaces of Euclidean space. The goal of the talk will be to see how isometric actions of circles and tori can be used to "recognize" the space on which they are acting.

Minimal Gaussian Partitions, Clustering Hardness and Voting (Steven Heilman, USC)

Emmy Noether Room, Millikan 1021, Pomona College 610 N. College Ave., Claremont, California

A single soap bubble has a spherical shape since it minimizes its surface area subject to a fixed enclosed volume of air.  When two soap bubbles collide, they form a "double-bubble" composed of three spherical caps.  The double-bubble minimizes total surface area among all sets enclosing two fixed volumes.  This was proven mathematically in a […]

Uniform asymptotic growth of symbolic powers (Robert Walker, University of Michigan)

Millikan 2099, Pomona College 610 N. College Ave., Claremont, CA, United States

Algebraic geometry (AG) is a major generalization of linear algebra which is fairly influential in mathematics. Since the 1980's with the development of computer algebra systems like Mathematica, AG has been leveraged in areas of STEM as diverse as statistics, robotic kinematics, computer science/geometric modeling, and mirror symmetry. Part one of my talk will be a […]