# Geometric Analysis and Topology Seminar

#### Kahler-Einstein Metrics on Fano Manifolds

**Speaker:**
Song Sun, Stony Brook

**Location:**
Warren Weaver Hall 517

**Date:**
Friday, November 1, 2013, 11 a.m.

**Synopsis:**

I will talk about joint work with Xiuxiong Chen and Simon Donaldson on the resolution of Yau's conjecture that a Fano manifold admits a Kahler-Einstein metric if and only if it is K-stable. We will motivate the definition of K-stability, outline the main idea and technical points involved in the proof. A key ingredient is to prove that under certain assumptions the Gromov-Hausdorff limit of a sequence of Kahler-Einstein manifolds has a natural structure of a normal projective variety, and an extension of this result to the case of metrics with cone singularities along a divisor.