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  • 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 […]

  • 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 […]

  • Saving Bats from Fungal Diseases with Linear Algebra (Nina Fefferman, U of Tennessee-Knoxville)

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

    Abstract: Bats in North America have been dying off due to the invasion of a fungal disease (White Nose Syndrome). In this talk, I'll present a very simple linear algebraic model to predict the magnitude of the die-offs. By comparing these models to some data about actual bat survival, my collaborator and I also hypothesized […]