Khintchine’s theorem on manifolds

Séminaire « Géométrie dynamique »
Orateur : Lei Yang (College of Mathematics, Sichuan University,  China)

Exposé online

Lieu : salle visio M3  

Résumé:  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 from 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.

Tweeter Facebook