Title: A thermodynamical formalism for Kähler-Einstein metrics on log Fano manifolds and applications

Speaker: Robert Berman (Chalmers University, Sweden)

Time: Apr 21, 2011, 2:00-4:00 pm

Venue: Room 1328 at BICMR, Resource Plaza, Peking University

Abstract: In this talk I will start by setting up a variational approach to rather general complex Monge-Ampère equations on a Kähler manifold X. The leading role wil be played by a certain "free energy functional", which generalizes Mabuchi's K-energy functional. Applications to Kähler-Einstein metrics on log Fano manifolds will then be given. In particular, inspired by a recent program of Donaldson in the context of the the Yau-Tian-Donaldson conjecture, it will be explained how to obtain Kähler-Einstein metrics on a Fano manifold which are singular along a given Calabi-Yau hyper surface.