Moy will continue his joint work with Barbasch investigating the unitary dual of a reductive p-adic group and will investigate with Hales certain ways to establish what is called a uniform germ expansion for orbital integrals. The research in unitarity, with a goal of classifying all unitary representations, will be to investigate certain basic representations called unipotent representations. The investigations in uniform germ expansions will be to find a way for determining whether two spaces of distributions are equal. The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics.
