Maximal ideals of reduced group C*-algebras

I will give a gentle introduction to C*-algebras, focusing on concrete C*-algebras attached to discrete groups. I will then explain a celebrated theorem by Kalantar and Kennedy that connects C*-algebra theory and geometric group theory. Explicitly, their theorem says that the reduced C*-algebra of a discrete group G is simple (meaning that {0} is the only proper, closed, two-sided ideal) if and only if the action of G on its Furstenberg boundary is free. Finally, I will mention recent joint work with Kevin Aguyar Brix, Kang Li, and Eduardo Scarparo where we extend the Kalantar–Kennedy theorem to parameterise maximal ideals in reduced group C*-algebras of discrete groups.

Venue: Fulton G20