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Explore rigidity and invariant measures in mathematical dynamics through this 47-minute lecture by David Fisher. Delve into two recent works that extend beyond homogeneous dynamics while utilizing tools from the field. Examine the applications to Zimmer's Conjecture and the study of totally geodesic submanifolds in real and complex hyperbolic manifolds. Gain insights into how invariant measures are investigated outside their traditional context, opening new avenues for understanding mathematical structures. Access accompanying slides for visual support and deeper comprehension of the presented concepts.