for this workshop
Analytic, arithmetic, and geometric aspects of automorphic forms
American Institute of Mathematics, Pasadena, California
Ashay Burungale, Mladen Dimitrov, Philippe Michel, and Chris Skinner
This workshop, sponsored by AIM and the NSF, will be devoted to problems and questions about the non-vanishing of automorphic periods, especially existence and potential applications. Past progress on such problems has found applications in works on the Birch--Swinnerton-Dyer conjecture, on non-vanishing of Iwasawa invariants of $p$-adic L-functions, and the finiteness of rational points on certain varieties. Of particular interest to this workshop will be the following topics:
- Analytic techniques to show non-vanishing of special values of L-functions that arise in the context of newly-constructed Euler systems.
- Automorphic periods related to arithmetic families of special cycles.
- The use of automorphic methods (such as the Gan–Gross–Prasad Conjectures) in the context of Diophantine problems for Shimura varieties.
This event will be run as an AIM-style workshop. 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.
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