Modul: MAT760 Ergodic Theory and Dynamical Systems Seminar

## Random walks by homeomorphisms on the line and orderability of lattices

Talk by Dr. Sebastian Hurtado

Speaker invited by: Prof. Dr. Alexander Gorodnik

**Date:** 02.03.20 **Time:** 13.45 - 14.45 **Room:** Y27H28

The standard random walk in the integers is known to be recurrent, it passes through any integer infinitely many times. We will discuss a generalization of this theorem for random walks given by homeomorphisms of the line due to Deroin-Navas-Kleptsyn-Parwani and discuss some applications to the theory of left-orderable groups. Our main result is that cocompact lattices in simple Lie groups of higher rank are not left-orderable groups (as a consequence, do not act by homeomorphisms in the line or the circle), a conjecture due to Witte-Morris and Ghys. The proof makes use of of higher-rank hyperbolic dynamics and some basic notions in infinite ergodic theory. (Joint work with Bertrand Deroin)