05/11: Sebastian Hurtado
Random walks by homeomorphisms on the line and left-orderability of lattices
Abstract: The standard random walk in the integers is known to be recurrent, it passes through every integer infinitely many times. We will discuss a generalization of this theorem for random walks given by random composition of homeomorphisms of the line (due to Deroin-Navas-Kleptsyn-Parwani) and some applications of this theorem to the theory of left–orderable groups. Our main result is that a lattice in a real semi-simple Lie group of higher rank and finite center is not a left–orderable group (equivalently, every action of such lattice in the line by homeomorphisms is trivial), a conjecture due to Witte-Morris and Ghys. (Joint work with Bertrand Deroin).