Mathematics

Geometric Analysis is by nature a field at the intersection of different branches of Mathematics. As such, it gathers the interest of specialists with a diverse set of expertise. Our group reflects this fact, as it is formed by colleagues with backgrounds ranging from analysis on non-smooth spaces to geometric flows, from Lorentzian geometry to optimal control problems. These complementary visions share a common research interest: the desire of studying singular geometric structures as a mean to better understand more regular ones. Here `structure’, `singular’, `regular’ are purposely vague terms, as our interests span broad areas of knowledge: for instance, we study metric measure spaces carrying weak curvature bounds as a tool to understand degeneration of smooth Riemannian metrics; as another example, geometric evolutions tend to develop singularities, that we study with the intent of capturing the geometry of evolving shapes.