Alessio FIGALLI — On the Monge–Ampère equation

The Monge–Ampère equation is a nonlinear PDE arising in several problems in the areas of analysis and geometry, such as the prescribed Gaussian curvature equation, affine geometry, optimal transportation, etc. In this talk I will first give a general overview of the classical theory, and then I will discuss some of the most recent and important developments on this beautiful topic.