Mathematical Sciences: Cohomology of G/P and Representation Theory of G, for Real Reductive Lie Groups and Generalizations

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Casian will study the problem of computing the cohomology of the flag variety for real reductive Lie groups, the cup product and Weyl group action, using the representation theory of the group. He will investigate the problem of determining which Schubert cells contribute to the non torsion part in homology. He will also investigate similar problems in the Kac-Moody setting. 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.