THEMATIC PROGRAMS

Thematic Program on Automorphic Forms

January - June 2003

Organizers:

James Arthur, University of Toronto Thomas Haines, University of Maryland Henry Kim, University of Toronto

Ram Murty, Queen's University George Pappas, Michigan State University Freydoon Shahidi, Purdue University

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Overview:

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.

Coxeter Lecture Series

March 10, 11, 12, 2003, 3:30 pm
Stephen S. Kudla (Maryland)
Arithmetic theta series

Distinguished Lecture Series

April 9, 10, 11, 2003, 3:30 pm
Peter Sarnak (Princeton)
Automorphic L-functions and equidistribution

Courses:

January 21 - May 1, 2003
Course on Automorphic L-functions ( Tues. & Thurs., 1:30 pm- 3:00 pm)
Instructors: H. Kim and R. Murty

• Tuesday 1:30 - 3:00 pm
  Course on Automorphic Functions
  Instructor: H. Kim

• Thursday 10:30 am- 12:00 pm
  Course on Symmetric Power L-Functions And Applications To Analytic Number Theory
  Instructor: R. Murty

January 21- April 29, 2003, Tuesdays 10:30 am - 12:00 pm
L-functions, Converse Theorems, and Functoriality for GL(n)
Speaker: Jim Cogdell (Oklahoma State)

Workshops:

March 4-8, 2003
Workshop on Shimura varieties and related topics
Organizers: T. Haines (Maryland) and G. Pappas (Michigan State)

May 5-9, 2003
Workshop on Automorphic L-functions
Organizers: H. Kim and R. Murty

Summer School

June 2-27, 2003
Clay Mathematics Institute Summer School on Harmonic Analysis, The Trace Formula and Shimura Varieties
Organizers: James Arthur (Toronto), David Ellwood (Boston & CMI), Robert Kottwitz (Chicago)

Postdoctoral Fellowships
Qualified candidates were invited to apply for postdoctoral fellowships associated with the program. Deadline for applications was January 2, 2002

Graduate Student Funding

Funding is available to graduate students to visit for a term. Interested graduate students must forward a letter of application with a letter of recommendation from their supervisor. Standard support amounts for graduate students is approx. $1000/mth. If requesting travel funding please include budget outlining costs. Students should negotiate with their home institutions or advisors for additional funding if required. All documents should be received by September 30, 2002 at the following address:

Thematic Program Coordinator- Automorphic Forms
Graduate Student Funding,
The Fields Institute 222 College Street, Second Floor
Toronto, Ontario, M5T 3J1, Canada.
Phone: (416) 348-9710
Fax: (416) 348-9759
Email: automorphic@fields.utoronto.ca

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For more information please contact automorphic@fields.utoronto.ca