for this workshop
Functoriality and the trace formula
American Institute of Mathematics, San Jose, California
Ali Altug, James Arthur, Bill Casselman, and Tasho Kaletha
This workshop, sponsored by AIM and the NSF, 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.
The workshop will differ from typical conferences in some regards. 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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