6 jun 2019 -- 14:30
Aula Tricerri, DiMaI, Firenze
Abstract.
A fundamental problem in Kähler geometry is to look for canonical metrics on a Kähler manifold, where the world “canonical” means that the metric satisfies a curvature condition. Such geometric problem boils down to a complex non-linear PDE of Monge-Ampère type. In the last 50 years the study of the regularity of solutions of such equations has motivated a lot of works. I will give a survey of what is known in this direction (also in singular settings), emphasising how the developments in pluripotential theory were crucial in order to treat (singular) complex Monge-Ampère equations.