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Lecture 1: Einstein metrics and linear group actions | Einstein Institute of Mathematics

Lecture 1: Einstein metrics and linear group actions

Date: 
Thu, 13/11/201414:30
Location: 
Lecture Hall 2
Lecturer: 
Prof. Gang Tian, Princeton University and Peking University
The study of Kähler-Einstein metrics was initiated by E. Calabi in the 50's. In the 70's, Yau's celebrated solution of the Calabi conjecture yielded the existence of Kähler-Einstein metrics with vanishing first Chern class. Aubin and Yau solved the existence problem for the case of negative first Chern class.

Since then, it has been a challenging problem to study the existence of Kähler-Einstein metrics on Fano manifolds. A Fano manifold is a compact Kähler manifold with positive first Chern class. There are obstructions to the existence of Kähler-Einstein metrics on Fano manifolds. Recently, the problem has been solved by relating existence to K-stability, a geometric stability generalizing substantially the stability from classical geometric invariant theory.

In the first lecture, I will first recall some known facts about Riemann surfaces. Then we give a brief tour on the study of Kähler-Einstein metrics in the last two decades. Next I will explain how those Einstein metrics are related to the study of algebraic group actions and geometric stability.

This lecture is aimed at a general audience.

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