报告人：Daniel Zhuangdan Guan（关庄丹）教授
报告题目：Recent progress on compact Kaehler-Einstein manifolds with cohomogeneity one metrics
摘要：Although there are many known Kaehler-Einstein manifolds, there is so far no very practical method to check a given compact Fano manifold to be Kaehler-Einstein or not.This is also true for the Kaehler metrics with constant scalar curvatures or Calabi extremal metrics. The situation for a cohomogeneity one metrics was completely resolved.For the type III case, it was solved in my dissertation in 1992. For the remain type I and II case, the existence is equivalent to the negativity of a topological integral.The type I case was published in 2011. Therefore, the problem is reduced to check the negativity for classes of Fano manifolds. Recently, we use computer to get some insight into a class of type I Fano manifolds. This work is a joint work with a group of students.
报告人简介：关庄丹（Daniel Zhuangdan Guan），加州大学河滨分校教授，1993年博士毕业于加州大学伯克利分校，师从著名的数学家S. Kobayashi，主要研究复几何，代数几何，齐性空间和辛几何。在国际著名杂志 Invent. Math.， Trans. of AMS等发表论文50多篇。