Measure doubling of small sets in SO(3,R)

par M. Chieu-Minh Tran (National University of Singapore)

jeudi 25 mai 2023, 16:00 → 17:00 Europe/Paris

Salle 112

Abstract: In a recent work, we show that if A is an open subset of SO(3,R) with sufficiently small normalized Haar measure, then

\mu(A^2) >3.99 \mu(A).

Our result was conjectured by Breuillard and Green around 2010 as a reaction to the so-called product theorems for groups of Lie type by Helfgott, Pyber-Szabo, and Breuillard-Green-Tao. In less precise forms, the question traces back to much earlier works of Henstock and Macbeath in the 50s.

 

In this talk, I will discuss this result and its proof highlighting the fact that  ideas from neostable group theory serve both as actual ingredients of the argument and as conceptual principles behind the stage. (Based on joint work with Yifan Jing and Ruixiang Zhang.)