#
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

## Original Announcement

This workshop 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).

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.

Papers arising from the workshop: