1 mar 2018 -- 15:00

Aula Dal Passo, Dip.Matematica, Università "Tor Vergata", Roma

**Abstract.**

A basic problem in geometry is to try to classify manifolds, the main object of study for geometers. The most well known example is the Uniformization Theorem that ensures that every orientable compact manifold of real dimension 2 admits a constant curvature metric. There are several ways to try and generalize the Uniformization Theorem in higher dimension. In this concerns, an interesting option is to restrict our attention to Kähler manifolds. The problem is then to study canonical metrics in Kähler geometry. Among those, the notion of Kähler-Einstein metrics is very important. In this talk we are going to introduce all these notions and we show how the study of special (=Kähler-Einstein) metrics gives insights into the classification of Kähler manifolds.