Abstract: Inspired by Margulis’ super-rigidity theorem about finite dimensional representations of lattices in higher rank semisimple Lie groups, Zimmer formulated the so-called Zimmer Program which calls for the study and potential classification of actions of higher rank semisimple Lie groups, and their lattices on manifolds. I will report on much recent progress, especially when the dynamics of the action is complicated, with lots of “hyperbolicity”.
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