Title: Carleson measures, uniform wrectifiability and $\varepsilon$-approximability of harmonic functions in $L^p$

Abstract: Uniform rectifiability is a geometric property that is strongly connected with harmonic analysis and elliptic PDE. Although many powerful PDE tools are not available in spaces with uniformly rectifiable boundaries, several authors have recently managed to prove positive PDE results in this general context. In this talk, we will discuss these results and talk about how an $L^p$ version of $\varepsilon$-approximability of harmonic functions can be used to characterize uniform rectifiability. The talk is based on joint works with Steve Hofmann and Simon Bortz.