Abstract:

In this talk I will introduce the study of lattices in locally compact groups through their actions on non-positively curved or CAT(0) spaces.  This is an extremely rich class of groups including S-arithmetic groups acting on products of symmetric spaces and buildings, right angled Artin and Coxeter groups acting on polyhedral complexes, Burger-Mozes simple groups acting on products of trees, and the recent CAT(0) but non biautomatic groups of Leary and Minasyan.  If time permits I will discuss some of my recent work related to the Leary-Minasyan groups.