New directions in nonlinear PDEs

The conference is designed to provide a week of intensive study and discussion on some of the most pressing themes in contemporary Nonlinear Analysis, engaging with a broad spectrum of mathematical problems characterized by their complexity and deep interconnections. The program is organized around key topics such as pattern formation in partial differential equations (PDEs), phase separation, optimal partition problems, shape optimization, and free boundary problems, together with the exploration of complex solutions to ordinary differential equations, particularly within celestial mechanics and Hamiltonian systems. Special attention is also devoted to singular perturbations and concentration phenomena.