# On the linearity of lattices in affine buildings (Geometry Day)

Date: Place: 18.11.2016 SR 0.014 (20.30) Jean Lécureux 11:30 - 12:30 Uhr

Abstract: Affine buildings are mostly useful because they admit nice actions by simple algebraic groups over local fields. However, there are some other constructions of 2-dimensional affine buildings, some of them with cocompact automorphism group.

After recalling the basic definitions and facts about affine buildings, I will explain the following theorem: a cocompact automorphism group of an $\tilde A_2$-building admits an infinite linear representation if and only if it is arithmetic. The proof uses ergodic techniques à la Margulis.

It is a joint work with Uri Bader and Pierre-Emmanuel Caprace.