My research is carried on in the area of mathematical analysis, and I am especially interested in questions concerning PDEs and the Calculus of Variations: in particular, I am interested in minimization problems and Gamma-convergence theory, geometric inequalities, free boundary problems, regularity theory, evolution equations. In the past, I've also been interested in Toeplitz matrices and their spectral distibution and, more generally, in the theory of structured matrices (I still enjoy these topics, but I am no longer working in this area as concerns research).
Some recent research lines along which I am active are the following. Together with Enrico Serra, we are exploring some new connections between defocusing hyperbolic equations and the Calculus of Variations, along the lines of some ideas originally suggested by De Giorgi through a conjecture, which we proved a few years ago (see here). Moreover, in collaboration with Riccardo Adami and Enrico Serra, we are studying the existence of ground states for the nonlinear Schroedinger energy functional over a metric graph, under a mass constraint (for some preprints, see here).
Some of my publications can be found here.