This research will focus on harmonic analysis. The emphasis will be on the orbit method of C(star)-algebras, including applications of these algebras to dynamical systems, to topology, and to the geometry of manifolds. One project is to develop new results on orbital integral formulas, symmetric spaces, and multiplicity questions in dynamical systems. The other project is a study of equivariant index theory, operator algebra invariants, and representations of discrete groups. This research is in the general subarea of modern analysis which examines the representation theory of algebras of functions.
