Angela Hicks, Lehigh University

Abstract

We'll talk about how representation theory can be used to determine fundamental questions about the rate of convergence of random walks on groups, and how the approach benefits from computer experimentation of eigenvalues of certain matrices. We'll also discuss some of the difficulties in this approach, here focusing on joint work with Daniel Bump, Persi Diaconis, Laurent Miclo, and Harold Widom studying a simple random walk on the the Heisenberg group mod p (a particularly simple to describe noncommutative group). Analysis of a random walk on the group dates back to Zach, who was considering the effectiveness of certain random number generators. We'll assume a bit of basic (undergraduate) group theory and probability, but otherwise aim for an elementary talk