中科院数学与系统科学研究院
数学研究所
学术报告
动力系统研讨班
报告人：杨磊（四川大学）
题 目：Khintchine’s theorem on manifolds
时 间：2022.09.15（星期四）16:00-17:00
地 点：腾讯会议：425 481 400会议密码：0915
摘 要：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.
个人简介：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 in high-quality peer-reviewed journals, which include Duke Mathematical Journal (advanced publication) and Geometric and Functional Analysis - GAFA (two papers: in 2019 and 2021).
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