GEOMETRIC ANALYSIS
AND POTENTIAL THEORY

ERC Advanced Grant

Grant agreement 101018680. This project aims to solve several long standing questions in geometric analysis by combining techniques from harmonic analysis, geometric measure theory, and free boundary problems.

Objectives

We are interested in the following areas: Metric and geometric properties of harmonic measure, like Hausdorff dimension. Caloric measure and parabolic singular integrals. The connection between square functions, like Carleson's square function, and rectifiability. Unique continuation at the boundary and free boundary problems. “