# What is a Foster-Lyapunov-Margulis Function?

Date: Mon, Nov 2, 2020

Location: University of Utah, Zoom

Subject: Mathematics

Class: Scientific

### Abstract:

We'll show how a simple idea from probability theory on the recurrence of random walks can be used in many important dynamical and geometric situations, building on work of Eskin-Margulis and others. No prior knowledge of probability theory, random walks, or geometry is required. If time permits, as an unrelated "dessert" of sorts, we'll give a brief proof of the Hopf ratio ergodic theorem using the Birkhoff ergodic theorem for flows.