School of Mathematics

Initiated by Langlands, the problem of computing the Hasse-Weil zeta functions of Shimura varieties in terms of automorphic L-functions has received continual study. We will discuss how recent progress in various aspects of the field has allowed the...

This is joint work with Tom Trogdon. Here the author shows how to prove universality rigorously for certain numerical algorithms of the type described in the first lecture. The proofs rely on recent state of the art results from random matrix theory...

I will introduce two notions that generalize the idea of real rootedness to multivariate polynomials: real stability and hyperbolicity. I will then show two applications of these types of polynomials that will (hopefully) be of interest to the CS...

I will give a brief overview of symplectic mapping class groups, then explain how one can use homological mirror symmetry to get information about them. This is joint work with Ivan Smith.

The determinant of an $n\times n$ matrix is an invariant polynomial of degree $n$ that is invariant under left and right multiplication with matrices in ${\rm SL}_n$. It generates in the sense that every other invariant polynomial is a polynomial...

This is joint work with Govind Menon, Sheehan Olver and Thomas Trogdon. The speaker will present evidence for universality in numerical computations with random data. Given a (possibly stochastic) numerical algorithm with random input data, the time...