题目：Recent Progress in Cohomogeneity One K\"ahler Einstein Metrics.
时间：March 16 (Friday) 4:30-5:30
Abstract: Although there are many known K\"ahler-Einstein manifolds, there is so far no very practical method to check a given compact Fano manifold to be K\"ahler-Einstein or not.This is also true for the K\"ahler 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 few classes of type I Fano manifolds. This work is a joint work with a group of students.
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