Diophantine Approximation and Random Walks on the Modular Surface

par Timothée Bénard (CNRS & Université Paris-Nord)

lundi 20 janv. 2025, 16:00 → 17:15 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

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).