中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

华罗庚青年数学论坛

综合报告

报告人：杨鹏宇 博士（ETH Zurich）

题  目：Equidistribution of translates of curves in homogeneous spaces and its applications to simultaneous Diophantine approximation

时  间：2021.07.16（星期五），16:00-17:00

地  点：数学院南楼N204室  腾讯会议：150 811 813

摘  要：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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  报告人：姜子麟 博士（Arizona State University）

题  目：Extremal Problems in Discrete Geometry

时  间：2021.07.23（星期五），10:00-11:00

地  点：数学院N219  腾讯会议：250 915 610

摘  要：What is the smallest total width of a collection of strips that cover a disk in the plane? How many lines through the origin pairwise separated by the same angle can be placed in 3-dimensional space? What about higher-dimensions? These extremal problems in Discrete Geometry look deceitfully simple, yet some of them remain unsolved for an extended period or have been partly solved only recently following great efforts. In this talk, I will discuss two longstanding problems: Fejes Tóth’s zone conjecture and a problem on equiangular lines with a fixed angle.
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  报告人：李时璋 博士（University of Michigan）

题  目：de Rham cohomology and p-adic Hodge theory

时  间：2021.07.30（星期五），09:00-10:00

地  点：数学院N219  腾讯会议：752 134 038

摘  要：从经典的德拉姆上同调出发，我们将介绍数学家们如何在p进几何（特别地，p进上同调理论）中不断地遇到德拉姆上同调的阿凡达。