Mathematical Sciences: Multivariate Orthogonal Polynomials and Hypergeometric Functions of Matrix Argument

该奖项支持古斯塔夫森教授的研究， 从事组合学研究 古斯塔夫森教授将在一门课上 由Askey和Wilson定义的正交多项式。 这些多项式的应用范围和量子物理一样广泛 和加法数论 建议明确 构造Askey-Wilson的多元推广 多项式表示的一个新的推广 矩阵自变量的超几何函数。 该研究是在组合学的一般领域。 组合数学试图找到有效的方法来研究如何 可以组织离散的集合。 离散的行为 系统对于现代通信是极其重要的。 为 例如，大型网络的设计，如电话系统， 计算机科学中的算法设计都涉及到 离散的物体，这就利用了组合研究。

This award supports the research of Professor Gustafson to work in combinatorics. Professor Gustafson will work on a class of orthogonal polynomials that were defined by Askey and Wilson. These polynomials have applications as diverse as quantum physics and additive number theory. It is proposed to explicitly construct multivariate generalizations of the Askey-Wilson polynomials expressed in terms of a new generalization of hypergeometric functions of a matrix argument. The research is in the general area of combinatorics. Combinatorics attempts to find efficient methods to study how discrete collections can be organized. The behavior of discrete systems is extremely important to modern communications. For example, the design of large networks, as in telephone systems, and the design of algorithms in computer science all deal with discrete objects, and this makes use of combinatorial research.