# Vortrag

Modul:   MAT760  Ergodic Theory and Dynamical Systems Seminar

## Khintchine’s theorem on manifolds

Vortrag von Dr. Lei Yang

Datum: 07.03.22  Zeit: 14.05 - 15.05  Raum:

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.