报告1：

题目: Counting rational approximations on grassmannians

报告人: Rene Pfitscher, 北巴黎大学

时间: 2025年4月22日9:00-10:00

地点: 数学科学学院(新楼) 310教室

摘要: In the divergence case of Khintchine's theorem, Schmidt obtained an asymptotic formula for the number of rational approximations of bounded height to almost every real number. Using exponential mixing in the space of lattices, we prove versions of this theorem for intrinsic diophantine approximation on grassmannians.

报告2：

题目: Super approximation for subgroups of SL_d(Z)

报告人: 张欣，香港大学

时间：2025年4月22日10:00-11:00

地点：数学科学学院(新楼) 310教室

摘要: It is a discovery of Margulis in 1970s that congruence quotients of SL_2(Z) can be used to construct expanders, which are certain sparse but highly connected graphs and are ideal models for network building.  The Super Approximation Conjecture of Salehi-Golsefidy and Varju gives a precise prediction on which more general subgroups of SL_d(Z) have this property. In this talk, I will survey the history of this conjecture, and describe a recent progress by Tang Jincheng and myself that all Zariski dense subgroups of SL_2(Z)×SL_2(Z) or SL_2(Z)×Z^2 have this property. This progress relies on the development of a key tool in arithmetic combinatorics conjectured by Salehi-Golsefidy.