Seminar: Prof M Lejmi
Abstract : Calabi defined the notion of extremal Kähler metrics in order to widen the problem of existence of Kähler Einstein metrics. For instance, the blow up of CP^2 at one point admits no Kähler metrics with constant scalar curvature but it does admit extremal Kähler metrics as shown by Calabi. Moreover, Calabi proved that the existence of extremal Kähler metrics imposes a certain decomposition of the Lie algebra of the automorphism group of the complex manifold.
I don't think that the talk will be really student-friendly since it needs some background from differential geometry. But I can do my best to define all the notions used in this talk.