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.
