His main research interest is geometric analysis, and in particular he studies problems with lack of compactness
and variational structure, approached with topological methods. 
He is the author of several scientific publications in the field, and of three volumes: Perturbation Methods and
Semilinear Elliptic problems on R^n, with A. Ambrosetti (Birkhauser, Progress in Mathematics, 2005), 
Nonlinear Analysis and Semilinear Elliptic Problems, with A. Ambrosetti (Cambridge Univ. Press, Cambridge Studies
 in Advanced Mathematics, 2007), Prescribing scalar curvature in conformal geometry 
(Zur. Lect. Adv. Math. EMS Press, 2023).

He graduated in Physics from the University of Milan and obtained his PhD from SISSA in Trieste.

He carried out postdoctoral studies at Rutgers University, the Institute for Advanced Study in Princeton and 
ETH Zurich. He was a professor at SISSA in Trieste and the University of Warwick before arriving at the 
Scuola Normale Superiore in 2015.