题目: Homogeneous dynamics, the slicing theorem and Khintchine's theorem on fractals

报告人: 张涵，苏州大学

时间: 10月22日（周二），10:00-11:00

地点: 五教5307

摘要: In 1984, Mahler proposed the following question on Diophantine approximation : How close can irrational numbers in the middle-thirds Cantor set be approximated by rational numbers?  One way to reformulate Mahler's question is to ask if Khintchine's theorem extends to the middle-thirds Cantor set.It turns out that random walks on homogenous sapces and slicing theorems in fractal geometry play crucial roles in answering Mahler's question. In this talk, I will survey works regarding Khintchine's theorem on fractals, discuss the connection between homogeneous dynamics and Diophantine approximation, and explain the idea of the proof of Khintchine's theorem on the middle-thirds Cantor set using tools from homogeneous dynamics and certain slicing theorem from fractal geometry.This is based on a joint work with Timothée Bénard and Weikun He.