|Location:||MSRI: Simons Auditorium|
Say that a group G involves all finite groups if for every finite group F, some finite index subgroup of G maps onto F.
For instance, for n>2, SL_n(Z) does not involve all finite groups, whereas Out(F_n) does for n>1. The family of groups Out(A) of outer automorphisms of right angled Artin groups "interpolates" between SL_n(Z) and Out(F_n), and the goal of this talk is to describe the boundary between these 2 behaviours, within this family of groups. We also study other "vastness" properties like SQ-universality, of having many quasimorphisms, and we prove that the boundary happens to be the same. This is a joint work with Andrew Sale.