Practice has shown that the combination of Harmonic Analysis, PDEs, Geometric Measure Theory and Complex Analysis is an extremely fertile and potent mix in the complex plane, with many notable achievements whose degree of technical sophistication is breathtaking. In sharp contrast with these successes the case of Several Complex Variables has been very little explored from the perspective of the latest advances of Harmonic Analysis and Geometric Measure Theory.

The aim of this talk is to discuss some recent progress in a program whose goal is to study the extent to which tools and methods from Harmonic Analysis, PDEs and Geometric Measure Theory may yield a qualitative upgrade of some of the most fundamental results in Several Complex Variables.