Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
Characterizing totally geodesic manifolds in negative curvature
The talk centers around the question of what invariant sets for Anosov flows and diffeomorphisms can look like. It is known that closed invariant sets can be arbitrarily bad and for example be fractals of arbitrary Hausdorff dimension. An old and interesting question, first raised by Hirsch in 1968 is what closed invariant submanifolds can look like. There are many surprising rigidity results in this direction, some quite old, and recently Rose Eliott Smith and I proved a new one, giving a dynamical characterization of totally geodesic submanifolds in negative curvature. I will explain the theorem and both the classical motivation and some more contemporary motivation. If time permits I will give some hints about the proof and particularly how it uses very old results from Smale and Mane.