ABSTRACT Speh/Barbasch In joint work the PI's will study the residual spectrum of the split classical groups. Barbasch will continue his research on unipotent representations for both real and p-adic groups, in particular their character theory and unitarity. Speh will continue her work with J.Rohlfs on the stabilisation of geometric invariants of locally symmetric spaces. 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.
