Mathematical Sciences: Research in Representation Theory andAutomorphic Forms

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Professor Wallach will continue his research in the general area of group representation theory. In particular his research will involve a generalization of the Kuznetsov formula and the Laplacian on locally symmetric spaces. In addition he will study the asymptotic behavior of Whittaker functionals in the theory of the Toda lattice and further projects in the area of direct integral decompositions of reducible real reductive groups. Group theory is basically the theory of symmetry. To take a simple example, when the system in question is invariant under a change in the position of the origin of space, the group of translations naturally arises. While groups are abstract objects, particular situations demand concrete realizations or "representations" of the symmetry group. Professor Wallach's investigations involve representations of groups which have geometrical or physical content.