Analytic, arithmetic, and geometric aspects of automorphic forms

January 29 to February 2, 2024

at the

American Institute of Mathematics, Pasadena, California

organized by

Ashay Burungale, Mladen Dimitrov, Philippe Michel, and Chris Skinner

Original Announcement

This workshop 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:

  1. Analytic techniques to show non-vanishing of special values of L-functions that arise in the context of newly-constructed Euler systems.
  2. Automorphic periods related to arithmetic families of special cycles.
  3. The use of automorphic methods (such as the Gan–Gross–Prasad Conjectures) in the context of Diophantine problems for Shimura varieties.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Workshop videos