State Polytopes of Combinatorial Neural Codes (Rob Davis, HMC)
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 […]
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Millikan 2099, Pomona College 610 N. College Ave., Claremont, CA, United States
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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 StatesAbstract: 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 […]
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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, CaliforniaLocust 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 […]
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The Bateman—Horn Conjecture, Part I: heuristic derivation (Stephan Garcia, Pomona)
Millikan 2099, Pomona College 610 N. College Ave., Claremont, CA, United StatesThe 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, […]
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Great Expectations (Matthew Junge, Duke Univ.)
Argue Auditorium, Pomona College 610 N. College Ave., Claremont, CA, United StatesThe 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 […]
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Isometric Circle Actions (Catherline Searle, Wichita State)
Argue Auditorium, Pomona College 610 N. College Ave., Claremont, CA, United StatesI 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 […]
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Minimal Gaussian Partitions, Clustering Hardness and Voting (Steven Heilman, USC)
Emmy Noether Room, Millikan 1021, Pomona College 610 N. College Ave., Claremont, CaliforniaA 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 […]
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Uniform asymptotic growth of symbolic powers (Robert Walker, University of Michigan)
Millikan 2099, Pomona College 610 N. College Ave., Claremont, CA, United StatesAlgebraic 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 […]
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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 StatesAbstract: 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 […]
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GEMS Workshop: Exploring the fascinating world of prime numbers, Part I with Professor Adolfo Rumbos, from Pomona College.
Shanahan 1480, Harvey Mudd College 301 Platt Blvd., Claremont, CA, United StatesTOPIC: Exploring the fascinating world of prime numbers, Part I The study of patterns in the sequence of prime numbers has fascinated mathematicians for centuries. Are there formulas that generate prime numbers? Are there patterns in the distribution of prime numbers and the distribution of gaps between consecutive primes? In this series of two workshops, beginning […]
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CFTP: the algorithm ERGM deserves, but not the one it needs right now (Matt Moores, University of Wollongong)
Emmy Noether Room, Millikan 1021, Pomona College 610 N. College Ave., Claremont, CaliforniaThe exchange algorithm enables Bayesian posterior inference for models with intractable likelihoods, such as Ising, Potts, or exponential random graph models (ERGM). Crucially, this algorithm relies on an auxiliary Markov chain to obtain an unbiased sample from the generative distribution of the model. It was originally proposed to use coupling from the past (CFTP) for […]
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Turning probability into polynomials (Mark Huber, CMC)
Millikan 2099, Pomona College 610 N. College Ave., Claremont, CA, United StatesMoment generating functions (Laplace transforms) are a means for transforming probability problems into problems involving polynomials. Here I will concentrate on the binomial distribution, and use the mgf to link […]