Pure Maths Colloquium - Lattices in products of trees and commensurators of free groups, Professor Pierre-Emmanuel Caprace (Université catholique de Louvain) Seminar

Event details

The study of lattices in products of trees was pioneered by D. Wise, and Burger-Mozes in the late 1990's. Their seminal works revealed that the class of finitely generated groups admitting a Cayley graph that is isomorphic to the Cartesian product of two trees is very rich: it contains not only products of virtually free groups, but also certain S-arithmetic groups and some finitely presented virtually simple groups, among many others. The goal of this talk is to overview this fascinating subject, emphasizing some key open problems. Time permitting, I will also present recent advances relying on the Classification of the Finite Simple Groups, and a connection to a question by Lubotzky-Mozes-Zimmer on commensurators of free groups.