The first half is an introduction to Kähler Geometry focusing on the problem of finding a Kähler metric of constant scalar curvature. We start with foundations of connections and curvature, and then review old and new existence results of Kähler-Einstein metrics and known obstructions such as K-stability. We will treat also Sasaki-Einstein metrics, and other generalizations of Einstein metrics. Toric manifolds will also be treated as a particular case.

Adjustment：The course on Oct. 9/23 changed to Oct. 11/18.

[1] A. Futaki : Kähler-Einstein metrics and integral invariants.

Springer Lecture Notes, vol. 1314, 1988.

[2] G. Székelyhidi : An introduction to extremal Kähler metrics, AMS, 2010.

[3] P. Gauduchon : Calabi's extremal Kähler metrics: An elementary introduction.

Zoom Meeting ID：849 963 1368   
Passcode: YMSC

https://us02web.zoom.us/j/8499631368?pwd=cHpiaXZBdS9abEpBbDZSeHJZNEU2UT09

Notes Download：

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