Mathematical Sciences: Algebraic, Geometric and Combinatorial Structures Related to Multivariate Hypergeometric Functions

数学科学：与多元超几何函数相关的代数、几何和组合结构

• 批准号: 9625511
• 负责人: Andrei Zelevinsky
• 金额: --
• 依托单位: Northeastern University
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9625511&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Algebraic; Geometric; Combinatorial

Zelevinsky This award provides funding for a project that will mainly be conducted in the following two areas: (A) Multivariate discriminants, resultants, and hyperdeterminants. (B) Representations of quantum groups and piecewise- linear combinatorics. Both of these subjects have deep relations with the theory of multivariate hypergeometric functions. Another unifying feature is that in both areas an essential role is played by new kinds of combinatorics whose main objects of study are lattice points in convex cones and polytopes and their piecewise-linear transformations. The principal investigator is going to continue his work on the following topics: (1) explicit polynomial formulas for multivariate discriminants and resultants, (2) singular loci of discriminant varieties, (3) algebraic and combinatorial properties of canonical bases in representations of quantum groups, (4) geometry of totally positive matrices, (5) Chow varieties of 0-cycles and symmetric functions in several vector variables, (6) secondary polytopes and maximal minor polytopes. This research explores connections between Combinatorics, Algebra, and Geometry. One of the goals of Combinatorics is to find efficient methods to study how discrete collections of objects can be arranged. The behavior of discrete systems is extremely important to modern communications. For example, the design of large networks, such as those occurring in telephone systems, and the design of algorithms in computer science deal with discrete sets of objects, and this makes use of combinatorial research.

泽列温斯基 该奖项为一个项目提供资金，该项目将主要在 以下两个方面：（A）多元判别式，结果，和超决定因素。(B)量子群的表示与分段线性组合数学。这两个学科都与多元超几何函数理论有着深刻的联系。另一个统一的特点是，在这两个领域中，新型的 主要研究凸锥和多面体中的格点及其分段线性变换的组合学。的 首席研究员将继续进行以下工作 主题：（1）多元判别式和结果式的显式多项式公式，（2）判别式簇的奇异轨迹，（3） 量子群，（4）全正矩阵的几何，（5）多向量变量的0-圈和对称函数的Chow簇，（6）次多面体和极大次多面体。 这项研究探讨了组合数学，代数， 几何组合数学的目标之一是找到有效的方法 来研究离散的物体集合是如何排列的。行为 对现代通信来说是极其重要的。为 例如，大型网络的设计，如电话网络中的网络设计， 系统，以及计算机科学中的算法设计处理离散 这就利用了组合研究。