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

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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.