My research mainly lies at the intersection of Calculus of Variations, Geometric Measure Theory and Nonlocal Equations.

In particular, I am interested in the regularity and qualitative behavior of nonlocal minimal surfaces, and especially of those which can be globally written as subgraphs, namely nonlocal minimal graphs.

Other topics that I have been studying are:

• free boundary problems

• phase transition/separation problems, like nonlocal versions of the Cahn-Hilliard system

• transport equations with nonlocal velocities, modeling both metric and topological interactions