Geometric Analysis and Potential Theory

The EU-funded GAPT project aims to solve several long-standing questions in geometric analysis by combining techniques from harmonic analysis, geometric measure theory and free boundary problems. These questions deal with harmonic measure and caloric measure, square functions and rectifiability and some related free boundary problems. In particular, the project will investigate a sharp bound for the Hausdorff dimension of harmonic measure and uncover the connection between the caloric measure associated with the heat equation and the parabolic rectifiability. Their study involves multiscale methods from the Littlewood–Paley theory and quantitative rectifiability.