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.