|December 10, 2013|
Thematic Program on Automorphic Forms
January - June 2003
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The theory of automorphic forms is a wide and deep subject touching many areas of mathematics. Our purpose is to concentrate on the geometric and analytic aspects of the subject. These have far-reaching applications in classical number theory. The Langlands-Shahidi method and the converse theorem of Cogdell-Piatetski-Shapiro have seen exciting new developments recently. These include new cases of functoriality, as well as analytic continuation of symmetric power L-functions. The work of Kim-Shahidi will be one of the central themes of the program.
The analytic theory of L-functions and its applications has also seen many advances in recent years. We hope to cover some aspects of these, especially those connected with the analyticity of symmetric power L-functions as well as those of Hasse-Weil zeta functions.
An important problem is to express the Hasse-Weil zeta function of a Shimura variety in terms of automorphic L-functions. Here in order to define the local factors not just at primes of good reduction, we need to study the variety at the finite set of primes of bad reduction. Such a description would allow one to apply the aforementioned progress in L-functions to the study of deep arithmetic properties of these varieties.
One of the major remaining obstacles to proving such a description is the so-called "fundamental lemma'' -- a conjecture in local harmonic analysis that asserts the equality of certain orbital integrals on a p-adic group and on a related (endoscopic) group. We plan to review recent work of Goresky-Kottwitz-MacPherson and others which gives a geometric approach to this problem.
March 10, 11, 12, 2003, 3:30 pm
April 9, 10, 11, 2003, 3:30 pm
Graduate Student Funding
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