Seminář z diferenciální geometrie pokračuje 2.12.2019 od 10:00 v učebně M5 Vincent Pecastaing (University of Luxembourg):Actions of higherrank lattices on conformal and projective structures Abstrakt: The main idea of Zimmer's program is that in realrank at least 2, the rigidity of lattices of semisimple Lie groups makes that their actions on closed manifolds are understandable. After a short survey giving a more precise idea of Zimmer's conjectures and their context, I will give recent results about conformal and projective actions of cocompact lattices. The fact that these geometric structures do not carry a natural invariant volume is one of the main motivations. We will see that the realrank is bounded above like when the ambient Lie group is acting, and that at the critical value, the manifold is globally isomorphic to a model homogeneous space. The proofs rely in part on an "invariance principle" recently introduced by Brown, RodriguezHertz and Wang, which guarantees the existence of finite invariant measures in some dynamical context.
