Mathematical Sciences: Representation Theory of Reductive Groups

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Professor Mirkovic will study the representation theory of real reductive groups using the ideas of perverse sheaves and D- modules. His program involves a number of projects, among them an attempt to prove a conjecture of Vogan involving characteristic cycles and a study of analytic localization of representations. 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.