Mathematical Sciences: Algebraic Combinatorics

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This award supports the research of Professor Philip Hanlon in the field of algebraic combinatorics. Hanlon will investigate a number of problems connected with two distinct subjects, the Macdonald Root System Conjectures and the inner product matrices defined by Varchenko in his work on representations of quantum groups and hypergeometric functions related to quantum groups. This research is in the general area of Combinatorics. Combinatorics attempts 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.