Subconvexity bounds for L-functions

This workshop, sponsored by AIM and the NSF, will be devoted to subconvexity bounds for L-functions. In recent years, there has been substantial progress towards the subconvexity problem for GL(2) L-functions, beginning with the work of Duke, Friedlander, and Iwaniec; more recently, ideas from representation theory and dynamics have been brought to bear on the problem. Subconvexity bounds for L-functions in higher rank (and, more generally, bounds for periods) remain largely elusive. The aim of the workshop is to consolidate the existing approaches and initiate analysis of the higher rank subconvexity problem.

The main goals for the workshop are

• Understanding the present approaches to subconvexity and their inter-relationships;
• Understanding the apparent "universality" of the Weyl exponent 1/6 and the Burgess exponent 3/16 (which seem to occur in many independent approaches)
• Paving the road towards subconvexity of higher rank L-functions and understanding applications this would have.

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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