Measure Rigidity Beyond Homogeneous Dynamics

Explore measure rigidity in dynamical systems beyond homogeneous spaces in this one-hour lecture by Simion Filip at BIMSA. Delve into the challenges of analyzing general dynamical systems and the importance of invariant measures. Learn about the groundbreaking measure and topological rigidity results for flows on homogeneous spaces associated with Lie groups, initiated by Margulis and Ratner. Discover recent advancements that extend similar rigidity properties to dynamical systems on manifolds under specific conditions. Gain insights into collaborative research with Aaron Brown, Alex Eskin, Federico Rodriguez-Hertz, David Fisher, and Ben Lowe, pushing the boundaries of our understanding of measure rigidity beyond homogeneous dynamics.