中科院数学与系统科学研究院

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)
  Homogeneous dynamics, the slicing theorem and Khintchine's theorem on fractals
  2024.10.15星期二1500-1600

 点:N913

  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.
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