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 […]
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 […]
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 […]
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 […]
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 […]
Moment 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 […]
Abstract: In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our […]
