Random covering and Littlewood Conjecture

Date/heure
16 octobre 2025
14:30 - 15:30

Lieu
Salle Döblin

Oratrice ou orateur
Andrei Shubin (Graz University of Technology)

Catégorie d'évènement
Séminaire de Théorie des Nombres de Nancy-Metz


Résumé

Assume that $\omega_1, \ldots, \omega_n$ are i.i.d. uniform random points in $[0,1]$, which serve as the centers of shrinking intervals of given lengths $\ell_1 \ge \cdots \ge \ell_n$. The Dvoretzky covering problem asks for necessary and sufficient conditions on the sequence $(\ell_n)$ under which these random intervals cover $[0,1]$ infinitely often, almost surely. The problem was solved in 1972 by Shepp, and his work has since been generalized in several directions.

In this talk, I will discuss some deterministic analogues of Shepp’s result and their applications to the Littlewood Conjecture.