21 apr 2016 -- 09:00
Aula Tricerri, DiMaI, Firenze
Abstract.
In this mini-course I will describe recent progress on complex Monge-Ampere equations on non-Kähler manifolds and applications to existence of special metrics. I will also include some details of the proofs and techniques. The mini-course is intended for a broad audience. In my first lecture I will discuss some background and motivation, and give an overview of the latest developments in this area. In the second lecture I will begin a discussion of the a priori estimates required to prove existence of solutions to these equations in the non-Kähler setting, starting with the "zero order" estimate. In the third lecture, I will talk about the key second order estimates for Monge-Ampère equations, and describe the difficulties arising from the non-Kähler torsion terms. Finally, I'll discuss some open problems in the field.