## Dr. Yumeng Ou (Dept. of Mathematics, University of Pennsylvania)

Abstract:

The Falconer distance conjecture (open in all dimensions) says that a compact set $E$ in $\mathbb{R}^d$ must have a distance set $\{|x-y|: x,y\in E\}$ with positive Lebesgue measure provided that the Hausdorff dimension of $E$ is greater than $d/2$. In this talk, we will describe some recent progress on this conjecture and several related questions concerning finite point configurations and the multiparameter distance problem.