数学研究所

学术报告

动力系统研究中心

报告人：张涵（苏州大学）

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

时  间：2024.10.15（星期二）15：00-16：00

地  点：N913

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.