Mathematical Sciences: Singular Unitary Representations and Cohomology of Arithmetic Manifolds

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DMS-9501092 PI: Li Li will investigate a new approach to the problem of exhaustion of automorphic forms based on recent work by Sarnak. This approach does not make use of Fourier coefficients and is applicable to groups of small rational rank, including anisotropic groups. It involves the study of matrix coefficients, small representations of p-adic groups, and some Diophantine problems. 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.