Segev Gonen Cohen

Actions of lattices on manifolds

In this talk we describe recent progress on the Zimmer Programme, the study of actions of lattices in Lie groups on manifolds by diffeomorphisms. We begin by recalling motivations and some important examples, explain the general strategy introduced by Brown-Fisher-Hurtado when the manifold is of low enough dimension, and discuss modifications that allow us to prove results in more general semisimple and S-arithmetic groups.