Mathematical Sciences: Multidimensional Hypergeometric Functions in Representation Theory and Conformal Field Theory

数学科学：表示论和共形场论中的多维超几何函数

• 批准号: 9203929
• 负责人: Alexander Varchenko
• 金额: $ 10.73万
• 依托单位: University of North Carolina at Chapel Hill
• 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 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9203929&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Multidimensional; Hypergeometric; Functions

The principal investigator will study the multidimensional hypergeometric functions and applications in representation theory and conformal field theory. He will use methods from partial differential equations and geometry to study representations of an arbitrary Kac-Moodey algebra and their quantum deformations. Other applications of the research in hypergeometric functions will be in the areas of algebraic geometry 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.

首席研究员将研究多方面的 超几何函数及其在表示中应用 理论和共形场论。他将使用来自 偏微分方程和几何学 表示的任意Kac-Moodey代数及其 量子形变研究的其他应用 超几何函数将在代数领域 几何学和代数K理论 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