# 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.