NSF/CBMS Regional Research Conference - Arrangements and Mathematical Physics - January 2002

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Hypergeometric functions have been the objects of mathematical study since the seventeenth century. Recent advances in the subject include the development of the Aomoto-Gelfand theory of multivariable hypergeometric functions. This theory is of particular interest in mathematical physics, with implications in the study of the Knizhnik-Zamolodchikov (KZ) differential equations from conformal field theory. In the Aomoto-Gelfand theory, a significant role is played by hyperplane arrangements, finite collections of codimension one affine subspaces of a complex vector space. The study of arrangements is a relatively new branch of mathematics on the interface between topology, algebra, algebraic geometry, combinatorics,and analysis.Professor Alexander Varchenko of the University of North Carolina will deliver a series of lectures entitled "Arrangements, Hypergeometric Functions, and KZ-Type Equations" at Louisiana State University. As thetitle indicates, in these lectures, Professor Varchenko will explain the role of hyperplane arrangements in the study of hypergeometric functions and equations of KZ-type. The lecture series, and surrounding discussion, will serve to crystalize recent research trends in arrangement theory deriving from connections with hypergeometric functions, and to focus attention on the outstanding important questions in this area and their applications. The lectures should be of interest to experts and students in all branches of arrangement theory, and to newcomers to the field as well.