第16期北京大学特别数学讲座，时间是2013.6.17-6.28，每周的一、三、五的下午14:00-16:00, 地点:数学中心全斋9教室.

李驰：本科和硕士毕业于北京大学数学学院，2007-2012在普林斯顿大学数学系师从田刚教授，现在在纽约州州立大学石溪分校做博士后研究。研究方向是复几何。

题目：Fano流形上Kahler-Einstein度量问题

大纲：最近Kahler几何中一个重要发展是Yau-Tian-Donaldson猜测的解决。这个猜测把Fano流形的解析性质和代数性质紧密地联系起来，对Fano流形的研究带来重要的信息。我们将讨论Kahler-Einstein度量问题中一些重要的概念和方法。这门简短的课程是陆志勤教授的Kahler几何课程的延续。以下是安排的内容。

1a: 引论：Kahler-Einstein度量问题和Tian的纲领. 1b: Futaki 不变量：解析定义.

2a: Futaki 不变量：代数定义. 2b: K-稳定性和Chow稳定性，有限维逼近.

3a: 能量泛函：Ding 泛函和Mabuchi 泛函. 3b: Moser-Trudinger 不等式.

4a:所有Kahler度量组成的空间的几何. 4b: Berndtsson的次调和性质定理：Kahler几何中的Brunn-Minkowski不等式.

5a: 带锥型奇点的Kahler-Einstein度量，log-Futaki不变量 5b: log-Ding泛函和log-Mabuchi泛函，容许角度的插值性质.

6: Yau-Tian-Donaldson 问题的解决（根据Tian的文章).

Peking University sixteenth special lectures in mathematics, the time : 2013.6.17-6.28, on Monday, Wednesday, Friday 14:00-16:00 , place : Mathematics center Quan Zhai 9 classroom.

Chi Li graduated from Peking University, obtaining Bachelor and Master degree. He studied at Princeton University from 2007-2012 under the supervision of Professor Gang Tian. He is now doing his postdoc research at State University of New York at Stony Brook. His main interest is Complex Geometry.

Title: Topics in Kahler-Einstein problem on Fano manifolds.

Abstract: These will be the follow-up topic lectures after Prof. Zhiqin Lu's course on Kahler geometry. We will discuss some key concepts and techniques in the problem of Kahler-Einstein metrics which lead to the recent resolution of Yau-Tian-Donaldson conjecture.

1a: Introduction/Review of Kahler-Einstein problem. 1b: Futaki invariant I: analytic definition.

2a: Futaki invariant II: Algebraic definition. 2b: K-stability and Chow stability, finite dimensional approximation.

3a: Energy functionals: Ding energy and Mabuchi energy. 3b:Moser-Trudinger inequalities.

4a: space of Kahler metrics. 4b: Berndtsson's subharmonicity theorem: Brunn-Minkowski inequality in Kahler geometry.

5a: Conical Kahler-Einstein metrics, log-Futaki invariant. 5b:log-Ding energy and log-Mabuchi energy, interpolation of cone angles.

6. Resolution of Yau-Tian-Donaldson conjecture (after Tian).