for this workshop
Geometric realizations of Jacquet-Langlands correspondences
American Institute of Mathematics, San Jose, California
Atsushi Ichino, Marc-Hubert Nicole, Kartik Prasanna, and Xinwen Zhu
This workshop, sponsored by AIM and the NSF, will be devoted to studying geometric realizations of Langlands functoriality via cycles on Shimura varieties. Recent progress in this area includes the work of Xiao-Zhu using cycles in the mod-p fibers of Shimura varieties and the geometric Satake isomorphism, and that of Ichino-Prasanna using (motivated) cycles in characteristic zero.
The goal of the workshop is to explore consequences of these recent advances, and possible generalizations.
Specific topics include:
- Understanding connections between the two approaches mentioned above, namely between the characteristic p methods and characteristic zero methods.
- Going beyond the "genericity" assumption in the characteristic p case, which is similar to a "rank one" assumption in the theory of special values of L-functions.
- Generalizing these constructions to other instances of functoriality.
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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