One of the central problems in kahler geometry is to find necessary and sufficient conditions for the existence of "canonical" metrics in a given kahler class. Thanks to Yau (and Aubin) , this has been solved for the first chern class, provided it is either negative or zero. Naturally, Much effort has been directed towards the case when the first chern class is positive. The general belief (primarily through the work of G.Tian) is that the existence of a K.E. metric (or more generally, a constant scalar curvature metric) is equivalent to the "stability" of the algebraic manifold. This should be veiwed as the fully nonlinear version of the Kobayashi Hitchin correspondence. I will give an account of progress on this problem, and discuss recent joint work with G.Tian.
Graduate students are especially encouraged to attend.