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

综合报告会

（Colloquium）

报告人：Nicolas de Saxcé(Université Sorbonne Paris Nord)   

题  目：Diophantine approximation and arithmetic groups

时  间：2024.01.10（星期三）15:30-16:30

地  点：数学院南楼N204

摘  要：Traditionally, diophantine approximation is the study of the distribution of rationals on the real line, or more generally, of rational points in R^n. After the work of Minkowski at the beginning of the 20th century, it became clear that much of the geometry underlying this problem could be described conveniently with lattices, i.e. discrete subgroups of maximal rank in a Euclidean space. More recently, Dani, Margulis, Kleinbock and their followers revisited this theory using dynamics on the space SL_d(R)/SL_d(Z) of lattices in R^d with covolume 1. The goal of the talk will be to explain how reduction theory for arithmetic groups allows one to present their ideas in a more general setting and, among other things, to answer some questions of Schmidt on rational approximations to linear subspaces in R^d.

报告人简介：Nicolas de Saxcé 于2012年在巴黎第十一大学取得博士学位，目前是法国索邦-巴黎北大学CNRS研究员。 他的研究兴趣非常广泛，涉及随机游走、李群上调和分析、测度论、齐性动力系统、丢番图逼近、量子遍历论等等。