Geometric Structures and Point Processes
Jayadev Athreya (University of Washington)
23-Sep-2021, 16:15-17:30 (3 years ago)
Abstract: In this talk, we will prove the convergence part of Khitchine’s theorem on non-degenerate manifolds. This confirms a conjecture of Kleinbock and Margulis in 1998. Our approach uses geometric and dynamical ideas together with a new technique of `major and minor arcs’. In particular, we establish sharp upper bounds for the number of rational points of bounded height lying near `major arcs’ and give explicit exponentially small bounds for the measure of `minor arcs’. This is joint work with Victor Beresnevich.
dynamical systemsnumber theory
Audience: general audience
New England Dynamics and Number Theory Seminar
Organizers: | Dmitry Kleinbock, Han Li*, Lam Pham, Felipe Ramirez |
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