#
Functoriality and the trace formula

December 4 to December 8, 2017
at the

American Institute of Mathematics,
San Jose, California

organized by

Ali Altug,
James Arthur,
Bill Casselman,
and Tasho Kaletha

## Original Announcement

This workshop will focus on various aspects of functoriality and automorphic
L-functions, with an emphasis on Langlands' proposal "Beyond endoscopy". The
proof of the fundamental lemma (notably by Ngo Bao Chau, building on work of
many others), and its variants, leading to the stabilization of the trace
formula by Arthur, has been fruitfully applied to obtain functoriality between
classical groups and GL(N). As these so-called endoscopic types of functoriality
are just a small fraction of general functoriality, this naturally leads to the
question of strategies and tools that may be used to attack more general cases
of functoriality. Recent papers of Langlands, Arthur, Ngo and others put forth
the trace formula and generalizations of Poisson summation formula as prominent
tools.
The goal of this workshop is to call attention to various aspects of
functoriality beyond endoscopy, and highlight problems that may conceivably be
within reach. The specific topics of discussion will include:

- Trace formula and its use in the study of the analytic properties of automorphic
L-functions,
- Stable transfer, and singularities of characters and orbital integrals,
- Analogues of the Poisson summation formula and functional equations of
automorphic L-functions,
- Basic functions and the geometry of monoids, and
- Other topics suggested by participants.

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.