Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Nicolas de Saxc ，Universit Sorbonne Paris Nord
Inviter:
Title:	Diophantine approximation and arithmetic groups
Language:	English
Time & Venue:	2024.01.10 15:30-16:30 南楼N204
Abstract:	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.