Mathematical Sciences: Mathematical Physics and Non- commutative Differential Geometry

数学科学：数学物理和非交换微分几何

• 批准号: 9207078
• 负责人: Ezra Getzler
• 金额: --
• 依托单位: Massachusetts Institute of Technology
• 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: 1992-07-01 至 1994-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9207078&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Physics; Non; commutative

The principal investigator will study applications cyclic homology and related algebraic constructions such as the deformation theory of algebras to quantum mechanics, microlocal analysis, index theory, and algebraic K-theory. 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.

主要研究人员将研究循环同调和相关的代数构造在量子力学、微域分析、指数理论和代数K-理论中的应用。该奖项将支持在微分几何和全球分析的一般领域的研究。微分几何是研究空间几何和定义在该空间上的解析概念之间的关系的学科。全局分析是通过拼凑局部信息来研究空间的整体几何和拓扑性质的学科。这些领域的数学在其他科学中的应用包括复杂分子结构、液体-气体边界和宇宙的大尺度结构。