Appears in collection : 2024 - T2 - WS3 - Actions of large groups, geometric structures, and the Zimmer program

Smooth rigidity of higher rank abelian and lattice actions with some hyperbolicity has been studied extensively. When the manifold is a nilmanifold, results by Rodriguez Hertz, Wang, and Brown, Rodriguez Hertz, Wang show that: If the action contains an Anosov diffeomorphism then the action is globally rigid. I will discuss rigidity of higher rank partially hyperbolic actions on nilmanifolds. In particular, I will discuss global rigidity of abelian and higher rank lattice actions that contain one fibered partially hyperbolic element.