This award supports the research of Professor Stephen Milne. His work will concentrate on the interrelationships among the fields of Combinatorics, Lie Algebras, and Hypergeometric Series. His principal goal will be to develop the theory and applications of his recent U(n) generalization of the Bailey Transform and the Bailey Lemma. This program has already led to the discovery and proof of many new theorems for multiple q-series and summations, connection coefficient theory, orthogonal polynomials, and related combinatorial applications. This research falls in the broad category of Combinatorics, which is one of the most active fields in today's mathematics. Fundamentally, Combinatorics represents a systematization of the very first of all mathematical activities, counting. In its modern development, however, Combinatorics has gone beyond just counting to make use of a wide variety of advanced mathematical techniques, and although its roots go back several centuries, the field has had an explosive development in the past few decades because of its importance in communications and information technology.
