Let SO3(ℝ) be the 3D-rotation group equipped with the real-manifold topology and the normalized Haar measure μ. Confirming a conjecture by Breuillard and Green, we show that if A is an open subset of SO3(ℝ) with sufficiently small measure, then μ(A2) > 3.99 μ(A).
This is joint work with Chieu-Minh Tran (NUS) and Ruixiang Zhang (Berkeley). This work relates to this arXiv paper.
This video is part of the Institute for Advanced Study‘s Special year research seminar.
