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Department of Mathematics,
Department of Mathematics,
University of California San Diego
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Math 288 - Probability & Statistics
Timothée Bénard
Université Sorbonne Paris Nord
Diophantine approximation and random walks on the modular surface
Abstract:
Khintchine's theorem is a key result in Diophantine approximation. Given a positive non-increasing function f defined over the integers, it states that the set of real numbers that are f-approximable has zero or full Lebesgue measure depending on whether the series of terms (f(n))_n converges or diverges. I will present a recent work in collaboration with Weikun He and Han Zhang in which we extend Khintchine's theorem to any self-similar probability measure on the real line. The argument involves the quantitative equidistribution of upper triangular random walks on SL_2(R)/SL_2(Z).
February 27, 2025
11:00 AM
APM 6402
Research Areas
Probability Theory****************************
