ALGB Seminar: Dawid Kielak (Universität Bielefeld)

Title: Property (T) for groups of automorphisms of free groups

Abstract: I will discuss Kazhdan's property (T), its relation to the spectral gap of the group Laplacian, and a recent recasting (by Ozawa) of the property using the group ring. I will then show how this new viewpoint can be used to derive a new proof of property (T) for SL_n(Z) (with n>2) and the first proof of (T) for Aut(F_n) (for n>4). This is joint work with M. Kaluba and P. Nowak.