#
Generalizing theta correspondences

July 28 to August 1, 2008
at the

American Institute of Mathematics,
Palo Alto, California

organized by

Wee Teck Gan and Gordan Savin

## Original Announcement

This workshop concerns extensions
and applications of the method of theta correspondence, including a
discussion of outstanding problems and future directions.
Specific topics include

- Exceptional theta correspondence. The setting of theta correspondence
was extended from the classical setting of metaplectic groups to the case of
other groups, most notably the exceptional groups.
- Restriction of small representations of classical groups. Some recent work of Ginzburg
and Ikeda uses small representations
to construct examples of CAP representations.
- Small representations of covering groups. In a recent work of
Bump-Friedberg-Ginzburg and Loke-Savin, small representations of covering groups of
orthogonal groups are constructed and then exploited to produce examples of liftings
- Backward lifting. This is a method pioneered by Ginzburg-Rallis-Soudry to
construct the backward lifting from $GL(n)$ to classical groups.
- Arithmetic applications. These include special values, non-vanishing and location
of zeros of L-functions, applications to p-adic L-functions as well as period
integrals and Gross-Prasad conjecture.

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.