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

主要研究人员将研究多维超几何函数及其在表象理论和保形场理论中的应用。他将使用偏微分方程和几何学的方法来研究任意Kac-Moodey代数的表示及其量子形变。超几何函数研究的其他应用领域将是代数几何和代数K-理论。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。

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.