Prof.  Zhuang-dan  Guan
University Of California,,  USA

Title: Homogeneous Spaces, Lie Groups and Complex Geometry

Abstract:

In this talk I will address some problems and developments with complex homogeneous spaces. In particular, we shall touch a recent problem of existing of sphere of six dimension type complex submanifolds in the 14 dimensional compact Lie group G2.

Biography:

I got my Master degree and studied complex geometry in the Institute of Mathematics, Academic Sinica with Professor ZhongJia Qing. I worked in the Institute for another year before I went to the United States. I got my Ph. D. in UCBerkeley with Professor Kobayashi as my advisor. I also worked with Professor Dorfmeister on complex homogeneous spaces. Although my major area is complex geometry, we use a lot of Lie algebra in our research. In the summer of 1993, I was able to find the first series of compact simply connected holomorphic symplectic manifolds starting with Kodaira-Thurston type of nilpotent Lie groups. That result settled a major problem in complex geometry for many years. And it was published in InventionesMathematicae. I also solved the existence of Kahler-Einstein metrics on compact cohomogeneity one complex manifolds and classified many compact complex homogeneous spaces.