# ALGB Seminar: Alain Valette (Université de Neuchâtel)

26/11/2018 - 16:00

Title: Kazhdan's property (T) and the group ring over the reals (after N. Ozawa)

Abstract: After a quick introduction to Kazhdan's property (T) and what it can do for you, we will move to a result by N. Ozawa (2013) who gave, for a finitely generated group G, the first characterization of property (T) in terms of group rings: G has property (T) if and only if there exists $\kappa>0$ and $x_1,...,x_n\in\mathbb{R}G$ such that $\Delta^2-\kappa\Delta=\sum_{i=1}^n x_i^*x_i$, where $\Delta$ is the Laplacian on some Cayley graph of $G$. This opened the way to checking property (T) on a computer; a recent success is property (T) for $Aut(F_5)$ (Kaluba-Nowak-Ozawa, December 2017).