Schmid and Bernstein plan to continue their study of the representation theory of reductive groups and Lie algebras from a variety of points of view. They plan to employ tools from topology, algebraic geometry, differential geometry, and analysis. The expected results, in turn, will have applications to geometry, number theory, and analysis. 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 and theoretical physics, especially quantum mechanics and elementary particle physics.
