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 […]
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 […]
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 […]
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 […]
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, […]
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 […]
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 […]
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 […]
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 […]
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 […]
TOPIC: 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 […]
The 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 […]
