The complex monge-ampère equation is an ubiquitous object in modern complex geometry. One famous instance of the importance of such equation is on Yau’s theorem that prescribes the Ricci curvature of Kähler metrics inside a cohomology class on compact manifolds.
In this talk, we’ll briefly discuss this theorem and have an overview of one of the modern proofs for it showcasing the importance of the study of solutions to the complex Monge-Ampère equation.
With that, as time allows, we’ll go on to discuss the importance of such type of results and what else a finer study of the Monge-Ampère equation, and degenerate versions of it, can give us in terms of geometry and how they relate to the geometry of singular spaces.
