# Stefan Witzel: Strong property (T) for ~A_2-lattices

**Time: **
Wed 2020-12-09 13.15 - 14.15

**Location: **
Zoom, meeting ID: 657 9019 8929

**Participating: **
Stefan Witzel, Uni Gießen

### Abstract

Kazhdan's property (T) is a rigidity property concerning unitary representations of a locally compact group on Hilbert spaces. Lafforgue's strong property (T) is a strengthening concerning more general representations on Banach spaces. Strong property (T) is known to hold for higher rank lattices by work of Lafforgue, Liao, de Laat, and de la Salle. It played a significant role in the recent solution of Zimmer's conjecture for SL_m(Z). I will speak about joint work with Jean Lécureux and Mikael de la Salle where we prove that cocompact lattices on ~A_2-buildings have strong property (T). These groups should be regarded as non-arithmetic relatives of lattices in SL_3(K) where K is a non-archimedean local field.

**Zoom Notes: **The meeting ID is 657 9019 8929 and the passcode is 3517257.