Past Events

In a previous lecture I waved my hands at the subject of period integrals for automorphic forms on SL_2. If that lecture had a point, it was that the phenomenon of non-vanishing of quadratic twists of L-functions was somehow related to the non...

Diophantine equations, one of the oldest topics of mathematical research, remain the object of intense and fruitful study. A rational solution to a system of algebraic equations is tantamount to a point with rational coordinates (briefly, a "rational...

Abstract: Diophantine equations, one of the oldest topics of mathematical research, remain the object of intense and fruitful study. A rational solution to a system of algebraic equations is tantamount to a point with rational coordinates (briefly, a...

How do simple local interactions combine to produce complex large-scale structure and patterns? The abelian sandpile model provides a beautiful test case. I'll discuss a pair of conjectures about the scale invariance and dimensional reduction of the...

We study the probability that the origin is connected to the sphere of radius R in critical percolation in high dimensions, namely when the dimension d is a large fixed constant, or when d>6 and the lattice is sufficiently spread out. I will present...

In this talk we present an algebraic context for knot theory. Knotted trivalent graphs (KTGs) along with standard operations defined on them form a finitely presented algebraic structure which includes knots, and in which many topological knot...

In the maximum likelihood mixture density estimation problem one is given a parametric family of densities and a data set. The question is then to find the regular Borel probability measure over the family's parameter space that yields the maximum...

This is the first talk of a series in Persistent homology

In 1960, Feit and Fine were interested in the question posed by the title and to answer it, they found a beautiful formula for the number of pairs of commuting n by n matrices with entries in the field F_q. Their method amounted to finding a...

We show that the catenoid is the unique surface of least area (suitably understood) within a geometrically natural class of minimal surfaces. The proof relies on a techniques involving the Weierstrass representation used by Osserman and Schiffer to...