Relative trace formula and periods of automorphic forms

August 24 to August 28, 2009

at the

American Institute of Mathematics, Palo Alto, California

organized by

Herve Jacquet, Erez Lapid, and Akshay Venkatesh

This workshop, sponsored by AIM and the NSF, will be devoted to the study of the relative trace formula and periods of automorphic forms.

In particular, we hope to formulate a precise general conjecture for the exact value of period integrals which encompasses all known cases (either proven, e.g. torus periods on GL(2) (Waldspurger), unitary periods on the general linear group (Jacquet), or conjectural e.g. the work of Ichino and Ikeda on the Gross-Prasad period). The relative trace formula relates periods integrals on two different groups, and often reduces a "difficult" period integral to an "easy" one, thus providing a powerful tool to attack the putative conjecture. Thus far the study of the RTF has been primarily example-based, and we hope to (begin to) develop a general theory.

The main topics for the workshop are

Examine all known cases of period integrals, with an eye towards formulating a general conjecture
Formulation of a "general" relative trace formula and its "compatibility" with the general conjecture.
Methodology of the relative trace formula: e.g. adapting the techniques of Ngo to relative setting, development of a local relative trace formula.
Examine the compatibility of the general conjecture with "explicit constructions" e.g. backward lifting, Theta.
Periods in the case where there is not multiplicity one (e.g. unitary and orthogonal periods on the general linear group).

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.

For more information email workshops@aimath.org

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