Tianyuan Mathematical Center
in Southwest China

2018 Thematic Program (III)

Singular Kahler-Einstein metrics

[TMCSC]

October 15-19, 2018

W303  School of Mathematics, Sichuan University

SPEAKER

A. Zeriahi (Institut de Mathematiques de Toulouse)

ABSTRACT

The goal of this course is to outline the proof of the solution of the Calabi conjecture by S.-T.Yau. This implies in particular the existence of a unique Kahler-Ricci flat metric in any given Kahler class on a compact Kahler manifold with trivial first Chern class.

We will also explain how Pluripotential theory allows to solve degenerate complex Monge-Ampere equations. A consequence is the extension of Yau's theorem and the existence of a singular Kahler-Ricci at metric on any projective variety with mild singularities and trivial first Chern class.

References

1. S.T.Yau: On the Ricci curvature of a compact Kahler manifold andthe complex Monge-Ampere equation. CPAM 31 (3) (1978), 139-411.

2. P.Eyssidieux, V.Guedj, A.Zeriahi: Singular Kahler-Einsteins metrics. JAMS 22 (2009), no 3, 607-639.

3. V.Guedj, A.Zeriahi: Degenerate complex Monge-Ampre equations. EMS Tracts in Mathematics, V. 26, 2017.

ORGANIZING COMMITTEE

Bohui Chen (Sichuan University)

Xiaojun Chen (Sichuan University)

Yuxin Ge (Institut de Mathematiques de Toulouse)

Li Sheng (Sichuan University)

SCIENTIFIC COMMITTEE

Jean-Pierre Demailly (French Academy of Sciences)

Vincent Guedj (Institut de Mathematiques de Toulouse)

An-Min Li (Sichuan University)

Xiangyu Zhou (Chinese Academy of Sciences)

FINANCIAL SUPPORT

ANR GRACK project

Institut de Mathematiques de Toulouse

Sichuan University

Tianyuan Fund for Mathematics

VIDEOS