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

This workshop, sponsored by AIM and the NSF, 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.

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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