Apparaît dans les collections : Algèbre, Géométrie et Physique : une conférence en l'honneur, Fields medallists - 1986

This will be mainly an expository talk. The Ding functional is an important notion in the study of Kahler-Einstein metrics and the Kahler-Ricci flow. Berndtsson showed that the Ding functional is convex in a certain sense, a result which has many important consequences. The main point of the talk will be to explain how the Ding functional and Berndtsson's result can be fitted into a general framework involvinga moment map for the action of the group of Hamiltonian diffeomorphisms. As far as time allows, we will explain some general background on existence problems for Kahler-Einstein and constant scalar curvature metrics and "stability" in algebraic geometry.