Geometric realizations of Jacquet-Langlands correspondences

November 11 to November 15, 2019

at the

American Institute of Mathematics, San Jose, California

organized by

Atsushi Ichino, Marc-Hubert Nicole, Kartik Prasanna, and Xinwen Zhu

Original Announcement

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 characteristic zero.

The goal of the workshop is to explore consequences of these recent advances, and possible generalizations.

Specific topics include:

  1. Understanding connections between the two approaches mentioned above, namely between the characteristic p methods and characteristic zero methods.
  2. 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.
  3. 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.