Jean Lécureux: Singular flow on affine buildings and group-theoretic applications
Affine buildings are mostly used because they are associated to algebraic groups over local fields. But there are also some other examples (which I will call "exotic") in dimension 2, some of them with interesting isometry groups.
My goal in this talk will be to explain some recent results on these exotic isometry groups, based on a new, ergodic-theoretic tool: the singular Cartan flow. Namely, we can prove that these groups are non-linear in a strong sense. Another application is to prove the Normal Subgroup Property : any normal subgroup is of finite index (this is an unpublished theorem of Shalom and Steger). This can also be generalized to prove rigidity of characters on the group (work in progress).
