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杨鹏宇 博士：Equidistribution of translates of curves in homogeneous spaces and its applications to simult

本站小编 Free考研考试/2021-12-26


Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars
Speaker: 杨鹏宇 博士，ETH Zurich
Inviter:
Title:
 Equidistribution of translates of curves in homogeneous spaces and its applications to simultaneous Diophantine approximation
Time & Venue:
 2021.07.16 16:00-17:00 南楼N204室 腾讯会议：150 811 813
Abstract:
 Consider the homogeneous space given by a semi-simple real algebraic group modulo a lattice subgroup. We study the distribution of expanding translates of a real-analytic curve by a diagonal flow, answering a question by Shah in ICM 2010, and earlier by Margulis in 2002 in a more general form. This result can be applied to show that on a “non-degenerate" real-analytic curve in the space of m*n real matrices, Dirichlet’s theorem on simultaneous Diophantine approximation cannot be improved for almost every point. Our approach is based on a tool from geometric invariant theory and Ratner’s measure rigidity theorem on Raghunathan’s conjecture.

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