Geometric realizations of Jacquet-Langlands correspondences
November 11 to November 15, 2019
American Institute of Mathematics,
San Jose, California
and Xinwen Zhu
This workshop 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
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
- Generalizing these constructions to other instances of functoriality.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
A list of open problems.