## Probability Seminar

**Date:** September 18, 2017

**Time:** 3:15PM - 4:14PM

**Location:** BLOC 220

**Speaker:** Boris Hanin, TAMU

**Title:** *Local Universality for Random Waves on Riemannian Manifolds*

**Abstract:** Random waves on a Riemannian manifold are a Gaussian model for eigenfunctions of the Laplacian. This model first arose in Berry's random wave conjecture from the 1970's, which states that random waves are good semiclassical models for deterministic wavefunctions in chaotic quantum systems. I will explain what this means and give some examples of why this conjecture is so far from being proved. I will then talk about some ongoing work with Yaiza Canzani about local universality for random waves. The idea is that, just like for random matrix models, random waves have universal scaling limits under some generic assumptions. This local universality allows one to say quite a bit about the size and topology (e.g. number of connected components) of zero sets of random waves. I will state some of these results and a few open questions as well.