This research is in the theory of Lie groups. This subject continues to expand as questions from geometry, number theory and physics continue to lead into it. Mostow's researches deal with lattices in Lie groups. Piatetski-Shapiro's work deals with L- functions aspects of Lie groups. Garland's project, in generalization of loop groups, is to study Chevalley groups over an arithmetic surface. Howe will study applications of the Heisenberg group to diverse parts of mathematics. This is a broad research program centered around the theory of Lie Groups. The applications will be in geometry, number theory and physics and possibly other areas of mathematics.
