Modul:   MAT760  Ergodic Theory and Dynamical Systems Seminar

Khintchine’s theorem on manifolds

Talk by Dr. Lei Yang

Date: 07.03.22  Time: 14.05 - 15.05  Room:

In this talk, we will prove the convergence part of Khintchine’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.