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Presented By: RTG Seminar on Geometry, Dynamics and Topology - Department of Mathematics

RTG SEMINAR GEOMETRY TOPOLOGY DYNAMICS: Arithmeticity, superrigidity, and totally geodesic submanifolds

Alex Maldague (Rice)

In 2018, Bader and Furman extended Margulis' higher-rank superrigidity theorem using the notion of algebraic representations of ergodic actions, abbreviated AREA. The idea now is to apply the AREA machinery in the rank-1 setting, where superrigidity remains a mysterious phenomenon. This talk will serve as a preview for my talk in the Geometry seminar, where I will discuss recent progress in this direction. In particular, I will review important elements of Margulis' original proof of superrigidity and provide some context for the recent work of Bader-Fisher-Miller-Stover on the arithmeticity of finite-volume hyperbolic manifolds with infinitely many maximal totally geodesic submanifolds.

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