Mathematical Sciences: The Structure of Cycle Spaces, Algebraic Manifolds, and Einstein Spaces

一个由四名几何学家组成的小组将调查各种各样的 复微分几何、黎曼几何、 和相关领域。 代数圈空间在 拓扑与同调-上同调的泛结构 理论将被仔细研究。 工作将在以下方面取得进展 建立Kahler-Einstein度规的存在， 流形，关于Moishezon中p-Kahler空间的结构 几何，以及黎曼4-流形的结构， 边界 调查小组将建立更多的地面 我们的四个物理学家的理解所必需的工作 三维时空 的分支之间的连接 数学广义上称为“微分几何”， 宇宙物理学可以追溯到爱因斯坦;数学 爱因斯坦应用的理论甚至可以追溯到高斯， 黎曼在世纪。在这里得到资助的团体 与物理学家保持密切联系，并引导他们的 在当前令人兴奋的方向进行研究， 数学家和物理学家

A team of four geometers will investigate a variety of problems in complex differential geometry, Riemannian geometry, and related areas. The role of spaces of algebraic cycles in universal constructions in topology and homology-cohomology theory will be carefully studied. Work will progress on establishing the existence of Kahler-Einstein metrics on open manifolds, on the structure of p-Kahler spaces in Moishezon geometry, and on the structure of Riemannian 4-manifolds with boundary. The team of investigators will establish more of the ground work necessary for the understanding by physicists of our four dimensional space-time. The connections between the branch of mathematics broadly referred to as "differential geometry," and cosmological physics dates back to Einstein; the mathematical theory which Einstein applied goes back even further to Gauss and Riemann in the nineteenth century. The group being funded here maintains close connections with physicists, and steers their research in directions of current excitement both to mathematicians and physicists.