Joseph HundleySIUC, Mathematics

The bulk of my work is in the RankinSelberg method, and much of it is joint with David Ginzburg. The RankinSelberg method is a method of studying the Dirichlet series with Euler product, known as L functions, which were attached by Langlands to automorphic representations of adele groups. Global applications to functoriality often involve characterizing the image of functorial lifts. My main current project with Ginzburg is an ambitious survey of the exceptional groups for such constructions. It is aided by some computer tools which I developed with my student Joe Pleso. In addition, I have recently completed an introductory textbook on automorphic forms on GL(n), with Dorian Goldfeld, and, together with E. Sayag, generalized the "functorial descent" construction of GinzburgRallisSoudry from representations which are isomorphic to their own contragredients to representations which are isomorphic to twists of their own contragredients.