Colloquium

A classical question in geometric measure theory, introduced by Falconer in the 80s is, how large does the Hausdorff dimension of a compact subset in Euclidean space need to be to ensure that the Lebesgue measure of its set of pairwise Euclidean distances is positive. In this talk, I will report some recent progress on this problem, which combines several ingredients including Orponen's radial projection theorem, and the refined decoupling theory.