Graduate Groups and Dynamics Seminar
Wouter van Limbeek
UIC
Spectral gap and almost diophantine groups, I (after Benoist-De Saxcé)
Abstract: We say a group of matrices in a compact Lie group has spectral gap if the associated averaging operator has eigenvalues bounded away from 1. This property is a geometric analogue of the algebraic criterion of expansion in Cayley graphs, and is intimately connected with a number of interesting problems such as construction of expanders and behavior of random walks. In this talk, we discuss a result of Benoist-De Saxcé connecting the spectral gap property to diophantine properties of matrices, and establishing spectral gap for groups with algebraic entries. This is the first of a series of talks on this result.
Tuesday September 25, 2018 at 3:00 PM in 1227 SEO