Mathematical Sciences: The Geometry of Cycle Spaces and Moduli Spaces

数学科学：循环空间和模空间的几何

• 批准号: 9204735
• 负责人: H. Blaine Lawson
• 金额: $ 21.4万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-08-01 至 1996-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9204735&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometry; Cycle; Spaces

The principal investigators will continue their investigation of problems in differential and algebraic geometry. In particular they will investigate the structure of Chow varieties via the method of characteristic classes. Results are expected to have relationships with Bott periodicity, the Hodge conjecture, and the Schubert calculus. This award will support research in the general area of differential geometry and global analysis. Differential geometry is the study of the relationship between the geometry of a space and analytic concepts defined on the space. Global analysis is the study of the overall geometric and topological properties of a space by piecing together local information. Applications of these areas of mathematics in other sciences include the structure of complicated molecules, liquid-gas boundaries, and the large scale structure of the universe.

主要调查人员将继续他们的 研究微分和代数几何中的问题。 特别是他们将调查的结构， 通过特征类的方法对品种进行分类。结果 预计与博特周期性，霍奇 猜想和舒伯特演算。 该奖项将支持一般领域的研究， 微分几何和全局分析。微分几何 是研究空间的几何形状 和空间上定义的分析概念。全球分析是 对物体的整体几何和拓扑性质的研究 一个空间，通过拼凑当地的信息。的应用 这些数学领域的其他科学包括 复杂的分子结构，液-气边界， 宇宙的大尺度结构