Freydoon Shahidi
Purdue

 

Functoriality Principle and the Spectral Theory of Automorphic Functions

                             Abstract:  In  these   two  lectures we start by explaining a number of   problems
                             in   arithmetic  and   spectral   theory   of   automorphic  functions  both   on   the
                             Poincare   and   Siegel   half   spaces   and   their  generalizations. We then show
                             how   they   can   be   resolved   by   appealing   to   certain   cases  of Langlands
                             functoriality  conjecture   which   allows   these   functions   to   be   transfered to
                             functions   on   spaces   of higher dimension in a canonical way.  These transfers
                             are   now established by the speaker and his collaborator in a number of   cases.
                             Our   discussion   will   include   the  recent developements on the conjectures of
                             Ramanujan   and Selberg for   Maass forms, as well as their generalizations   to
                             more general groups. We will also explain  how these results lead to new   cases
                             of Artin conjecture as well as to the existence of Siegel modular forms of weight
                             3   and   other  arithmetic and spectral results.    We  conclude  these lectures by
                             sketching    in    a   simple   language   how   these    transfers   are   established.

Thursday, April 21
312 Mathematics Building
This Lecture will be at 5:30 p.m.
Tea will be served at 4:45 p.m., in 508 Mathematics Bldg.

and

Friday, April 22
312 Mathematics Building
This Lecture will be at 4:30 p.m.
Tea will be served at 3:45 p.m., in 508 Mathematics Bldg.