Mathematical Sciences: Combinatorial Aspects of Representation Theory & the Theory of Symmetric Functions

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This award supports the research of Professor A. Garsia to work in combinatorics. He intends to investigate representations of finite reflection groups, in particular, problems derived from studying the Macdonald basis. He will also study orbit harmonics and graded representations and the q,t-Kostka coefficients of bigraded modules. The research is in the general area of combinatorics. Combinatorics attempts to find efficient methods to study how discrete collections of objects can be organized. And, so it 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.