Séminaire Géométrie et groupes discrets

Diophantine Approximation and Random Walks on the Modular Surface

by Timothée Bénard (CNRS & Université Paris-Nord)

Europe/Paris
Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane

IHES

Le Bois Marie 35, route de Chartres CS 40001 91893 Bures-sur-Yvette Cedex
Description

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). 

Organized by

Fanny Kassel

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