报 告 人：杨磊 副研究员
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.
报告人简介：Lei Yang is an associate professor at Sichuan University. He got his PhD at Ohio State University with Nimish Shah in 2014 and held postdoc positions at Yale (with Margulis, Fall, 2014), MSRI (Spring, 2015), and Hebrew University (with Lindenstrauss, 2015-2017), before moving to Sichuan. His research focuses on homogeneous dynamics and their applications to Diophantine approximation. With collaborators, he has made serious progress on several topics in Diophantine approximation, including badly approximable vectors, and multiplicative Diophantine approximation. His achievements in these areas have been published/accepted in high quality peer reviewed journals, which include Duke Mathematical Journal (accepted paper) and Geometric and Functional Analysis - GAFA (two papers: in 2019 and 2021).