Free boundary and PDE analysis – BLADE-JC

Seemingly distant problems in Geometric Analysis – ranging e.g. from harmonic maps theory and its generalizations to prescribed
curvature problems – share strong, common features: conformal invariance properties, existence of conservation laws, min-max
phenomena are some examples of them. The systematic development of asymptotic analysis techniques, in recent years, has led to
spectacular results in Geometric Analysis and to a better comprehension of the underlying analytical structures at work. This project
aims at bringing together promising young researchers with a solid background in complementary areas of Asymptotic and
Geometric Analysis, to share their expertise into an ambitious research program. The goal is to achieve significant progress in
several active and exciting research areas such as free-boundary minimal surfaces, Poincaré Einstein-metric, Equations of
Ginzburg-Landau type and constraint equations in General Relativity