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Modular forms for SL(3,Z)

Mathematical Physics & Probability

Speaker: Stephen Miller, Rutgers University
Location: 693 Kerr
Start time: Tue, May 27 2003, 3:10PM

I'll give a survey of what's known about modular/automorphic forms on SL(3,Z)\SL(3,R), and somewhat also for SL(n,Z)\SL(n,R). These spaces generalize quotients of the upper half plane by SL(2,Z), and are home to the most general types of automorphic forms in existence (at least according to conjectures of Langlands). After explaining the basic definitions, history, relations to classical number theory, and important open problems, I'll delve into various topics related to eigenvalue problems, and to the group cohomology of SL(n,Z).