The field of automorphic representations is a meeting ground of various branches of mathematics -- for example, number theory, Lie theory, algebraic geometry -- and of mathematical physics. Its origins are found in the attempt to apply the techniques of infinite-dimensional representation theory of groups to obtain a deeper understanding of L-series, a dominating concept in number theory. As a subset of representation theory, great progress has been made in the past few decades. Thus, one now finds a remarkable expanse of technique and applications involving the analytic theory of modular forms, trace formulas, techniques of algebraic geometry, combinatorics, and functional analysis. The research of Professor Flicker deals with the transfer of automorphic representations between two groups. Recent collaborative work establishes the metaplectic correspondence relating automorphic forms on the general linear group and an arbitrary topological covering. This work develops new techniques while also simplifying computations. Various applications of these results comprise Professor Flicker's subsequent work. Current plans call for work in several directions: Lifting theorems for automorphic forms. Transfer of stable orbital integrals. Matching of orbital integrals of smooth functions. Computations of characters and twisted characters. Trace formulas. Ramanujan conjecture for GL(n) over a function field. Congruence relations. Applications of the Hecke algebra with respect to an Iwahori subgroup.
