Mathematical Sciences: Homogeneous Complex Manifolds and Isoparametric Hypersurfaces in Spheres and Nonlinear PartialDifferential Equations

约瑟夫·多夫迈斯特将在三个领域进行研究。这些问题涉及齐次复流形、球面上的等参超曲面和非线性偏微分方程组。Dorfmeister与Nakajima和Neher合作，最近在齐次Kahler流形和某些等参三系方面取得了显著的结果。他将继续应用代数和泛函分析技术来解决相关问题。特别地，他将尝试确定流形上允许自同构群传递的所有Kahler结构。第二个主要项目是描述作为齐次Kahler流形的无穷小自同构出现的所有李代数。程序的最后部分涉及到复n维空间中一类可压缩的、有理的、齐次的区域的研究。

Josef Dorfmeister will carry out research in three areas. These concern homogeneous complex manifolds, isoparametric hypersurfaces in spheres and nonlinear partial differential equations. Dorfmeister, in collaboration with Nakajima and Neher has recently achieved remarkable results concerning homogeneous Kahler manifolds and certain isoparametric triple systems. He will continue to apply algebraic and functional analytic techniques to related problems. In particular he will try to determine all Kahler structures on manifolds which admit a transitive group of automorphisms. The second major project will be to describe all Lie algebras which occur as infinitesimal automorphisms of some homogeneous Kahler manifold. The final part of the program concerns an investigation of the class of contractible, rational, homogeneous domains in complex n-dimensional space.