Tim Austin: Notions of entropy in ergodic theory and representation theory

Location

FR4 (Oskar Klein), Albanova

Schedule

14:15–15:00 Pre-colloquium by Kirthana Rajasekar in FB54.

15:15–16:15 Colloquium lecture by Tim Austin.
16:15–17:00 SMC social get together with refreshments.

Abstract

Entropy has its origins in thermodynamics and statistical mechanics. It was explored with mathematical rigour in Shannon's work on the foundations of information theory, and quickly found striking applications to ergodic theory in work of Kolmogorov and Sinai. Many variants and other applications have appeared in pure mathematics since, connecting probability, combinatorics, dynamics and other areas.

I will survey a few recent developments in this story, with an emphasis on some of the basic ideas that they have in common. I will focus mostly on (i) Lewis Bowen's "sofic entropy", which helps us to study the dynamics of "large" groups such as free groups, and (ii) a cousin of sofic entropy in the world of unitary representations, which leads to new large deviations principles for tuples of random matrices.