Harmonic Analysis on Uniformly Rectifiable Sets and Applications to Complex Analysis of a Single and Several Variables

In this talk I will discuss recent developments at the interface between Harmonic Analysis and Geometric Measure Theory (Calder\'on-Zygmund theory on Uniformly Rectifiable sets, a sharp divergence theorem with non-tangential boundary traces, Fatou-type theorems, etc.) and present their impact in problems arising in Complex Analysis, of a single and several variables, which make systematic use of singular  integral operators.