New improvement to Falconer’s distance set conjecture in higher dimensions

Falconer’s distance set conjecture says that a compact set in $\mathbb{R}^d$ whose Hausdorff dimension larger than $d/2$ must have a distance set of positive measure. The conjecture is still open in all dimensions. In this talk, I’ll discuss some recent progress towards it in dimension three and higher, which involves new techniques from the theory of radial projections and decoupling. This is based on joint works with Xiumin Du, Kevin Ren, and Ruixiang Zhang.