In-Person and Online Talk 

A celebrated theorem of Freudenthal and Hopf says that a finitely generated group has 0, 1, 2 or infinitely many ends. The goal of this talk is to introduce the related notion of end invariants of a space or finitely generated group, their connection to a notion of (co)-homological duality introduced by Bieri–Eckmann, and discuss the particular case of the outer automorphism group of a free product of finite and cyclic groups.