报告人：Daniel Zhuangdan Guan（关庄丹）教授
报告题目：Recent Progress in the classification of complex homogeneous spaces
摘要：A manifold M is a homogeneous space if M=G/H with G a finite dimensional group and H a closed subgroup. M is a complex homogeneous space if J is the given complex structure on M such that J is invariant under the action of G. Homogeneous space is a classical area of differential geometry.The most famous work was the classification of real (and complex) semi-simple Lie groups and the symmetric spaces. The Kaehler homogeneous space was classified by Dorfmeister and Nakajima in 1988. The pseudo-kaehler homogeneous space with reductive G was classified by Dorfmeister and Guan in 1989. In the general compact complex homogeneous case, the classification reduced to the parallelizable case, i.e., in which H is discrete. In the late 1990's we proved that if G/H is a compact complex parallelizable manifold,then the semi-simple part of G is locally a product of complex simple Lie group of type A.A classification of the compact complex homogeneous space with an invariant volume was also finally classified.A complete classification of the compact complex space with a pseudo-keahler structure (non-necessary invariant) was given in 2007. Recently, compact complex homogeneous space with an invariant locally conformal Kaehler structure was classified and similarly for the cohomogeneity one case.
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。