Mathematical Sciences: Parametrization of Supercuspidal Representations of Reductive Groups Over Local Fields, and Related Topics

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This project is mathematical research in the representation theory of reductive groups over local fields. Although these groups are totally disconnected, their study is related to that of Lie groups, the smooth groups of symmetries studied by many analysts. There is a substantial interface with algebra and number theory as well. More specifically, the program of Professor Morris is to investigate the relationship between the harmonic analysis of such a group and the representations of the Galois group of the algebraic closure of the underlying field. A major part of this endeavor is to understand the conjectured correspondence for the supercuspidal representations, and to parametrize them.