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

自17世纪以来，超几何函数一直是数学研究的对象。该学科的最新进展包括多元超几何函数的Aomoto-Gelfand理论的发展。这一理论在数学物理中特别有意义，它对从保形场理论研究Knizhnik-Zamolodchikov(KZ)微分方程具有重要意义。在Aomoto-Gelfand理论中，超平面排列扮演着重要的角色，超平面排列是复向量空间的余维一仿射子空间的有限集合。排列的研究是在拓扑学、代数、代数几何、组合学和分析之间的一个相对较新的数学分支。北卡罗来纳大学的Alexander Varchenko教授将在路易斯安那州立大学做一系列题为《排列、超几何函数和KZ型方程》的讲座。正如题目所示，在这些讲座中，Varchenko教授将解释超平面排列在研究超几何函数和KZ型方程中的作用。这一系列讲座和相关讨论将有助于阐明超几何函数联系所衍生的排列理论的最新研究趋势，并将注意力集中在该领域的突出重要问题及其应用上。这些讲座应该引起编排理论所有分支的专家和学生的兴趣，也应该引起该领域的新手的兴趣。

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.