
Name: Ben McReynolds (Purdue University)
Title: Profinite completions and lattices in Lie groups
Abstract: The profinite completion of a finitely generated, residually finite group is the universal group for the finite representation theory of the group. One of the basic questions one can ask is whether or not the group is determined up to isomorphism by its profinite completion. Said alternatively, when is a finitely generated, residually finite group determined by its finite quotients. In this talk, I will discuss some positive and negative results to this question with the main focus on lattices in Lie groups. This is based on recent work with Martin Bridson, Alan Reid, and Ryan Spitler.