Mathematical Sciences: Arithmetic, Geometric and Ergodic Aspects of the Theory of Lie Groups and their Discrete Subgroups

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DMS-9424613 PI: Margulis Margulis will investigate the dynamics of subgroup actions on homogeneous spaces with applications to number theory, properly discontinuous groups acting on homogeneous spaces, rigidity questions and related problems in geometry and ergodic theory, and geometric aspects of reduction theory. 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.