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

该奖项支持Gustafson教授在组合学方面的研究。古斯塔夫森教授将研究一类由阿斯基和威尔逊定义的正交多项式。这些多项式有各种各样的应用，如量子物理和加性数论。提出了用矩阵参数的超几何函数的一种新推广来显式构造Askey-Wilson多项式的多元推广。这项研究是在组合学的一般领域。组合学试图找到有效的方法来研究如何组织离散集合。离散系统的行为对现代通信极为重要。例如，大型网络的设计，如电话系统，以及计算机科学中算法的设计都涉及离散对象，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.