Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
Keywords and Mathematics Subject Classification (MSC)
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No Notes/Supplements Uploaded No Video Files UploadedIn Margulis's thesis, he used mixing of the geodesic flow to prove the prime geodesic theorem which gives an asymptotic formula for the number of primitive closed geodesics according to their lengths in a closed hyperbolic manifold, i.e., for uniform lattices in SO(n, 1). A power-saving error term was obtained for convex cocompact subgroups by Naud and Stoyanov. It is natural to seek generalizations in the higher rank setting such as SL(n, R). Sambarino obtained a prime orbit theorem without an error term for Anosov subgroups. In a joint work with Michael Chow, we go further and establish exponential mixing of an appropriate dynamical system and use that to obtain a power-saving error term.