报告地点：腾讯会议 ID：869 395 836
报告地点：腾讯会议ID：319 239 793
报告题目：Homogeneous dynamics and Khtinchine's theorem on manifolds
报告摘要：In these two talks, I will explain the proof of the Khintchine theorem for manifolds. We will prove that the Khintchine theorem holds for any non-degenerate manifolds, namely, convergence (and divergence, respectively) of a series involving the approximate function will imply that the set of approximable point (with respect to the approximate function) lying on a non-degenerate manifold has zero Lebesgue measure (and full Lebesgue measure, respectively). This confirms a conjecture by Kleinbock and Margulis in 1998 and strengthens their result in a sharp way.The first talk is devoted to a brief history of this topic. I will explain the detail of the proof in the second talk. This is a joint work with Beresnevich.