题目：Harmonic Analysis, PDE, and Geometric Measure Theory
摘要：In this short course, I will talk about the solvability of elliptic PDE on rough domains. The solvability is closely related to the geometry of domains and the absolute continuity properties of harmonic measure. Such connection goes back to the classical result of F. and M. Riesz in 1916, and has attracted considerable interest over the last century, with remarkable progress over the last two decades. We will focus on the geometry of sets, Dahlberg’s conjecture on non-connected sets, and the well-posedness of the Dirichlet problem on rough sets, respectively.