EVENT DETAILS AND ABSTRACT

Title: Monge-Ampère equations, variational principles and balanced metrics
Speaker: Robert Berman
Speaker Info: Chalmers Inst. of Technology
Brief Description:
Special Note:
Abstract:

n a very recent joint work with Sebastien Boucksom, Vincent Guedj and Ahmed Zeriahi a new variational approach to solving complex Monge-Ampere equations in big cohomology classes on a complex manifold X was developed. Applications to existence and convergence of "balanced metrics" were also investigated. In this talk I will in particular focus on these latter applications. It was Simon Donaldson who first proposed to use suitably defined balanced metrics as canonical "polynomial" approximations of (1) solutions of the inhomogenous Monge-Ampere equation for a metric on an ample line bundle L, given a measure on X (2) Kähler-Einstein metrics, when L is the (anti-) canonical line bundle.