Steven Zelditch

Title: Bergman metrics and the symmetric space of all Kahler metrics
in a fixed class.

Abstract: It was pointed out by Mabuchi, Semmes and Donaldson that
the space of all kahler metrics in a fixed class is formally an
infinite dimensional symmetric space. The geometry of this space is
important but difficult: For instance, its geodesics are solutions of
a homogeneous Monge Ampere equation. The infinite dimensional
geometry may be approximated by finite dimensional symmetric spaces
of Bergman (= Fubini-Study) metrics. We will discuss this
approximation and its applications. In particular, it is very
concrete for toric varieties.