Geometric Analysis and Topology Seminar

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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.