). This 2-day working workshop, aimed at reporting the latest progress on the subject, took place from May 11-13, 2015 in the Department of Mathematics at Purdue University.
Below, you will find a list of the abstracts and videos for the talks given at the workshop. Be warned that many of the videos are nearly 1 GB in size.
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- Introduction to L-Functions
- Freydoon Shahidi (Purdue University)
- Friday May 8 from 2:00 PM - 3:00 PM in MATH 731
- ABSTRACT: This talk is part of the introductory lectures given the Friday before the Beyond Endoscopy Workshop.
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- Introduction to the Trace Formula
- Abhishek Parab (Purdue University)
- Friday May 8 from 3:30 PM - 4:30 PM in MATH 731
- ABSTRACT: This talk is part of the introductory lectures given the Friday before the Beyond Endoscopy Workshop.
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- An Introduction to Beyond Endoscopy
- Jasmin Matz (Mathematical Institute, University of Leipzig, Germany)
- Monday May 11 from 9:30 AM - 10:30 AM in BRNG 2290
- ABSTRACT: I could give an overview of Langlands' "Beyond Endoscopy". So my tentative plan would be to give a summary of part I & II of Langlands BE and then maybe elaborate on some of the points mentioned there - this depends a little on what the other participants plan to speak about. Two central points are probably to explain the problems of removing the contribution of the trivial representation on the geometric side of the trace formula, and of isolating the representations of Ramanujan type. However, I have not worked out any details yet.
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- Problems Beyond Endoscopy
- James Arthur (University of Toronto)
- Monday May 11 from 11:00 AM - 12:00 PM in BRNG 2290
- ABSTRACT: I shall speak on further questions related to my talk last year at Banff. These include the problems relating to the geometic contributions of spectral terms in what I called the stabilization of the (hypothetical) r-trace formula. Of particular interest are the nontempered spectral terms for (say) quasisplit orthgonal and sympletic groups. My talk would concern questions rather than answers!
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- Remarks on a Paper of Frenkel, Langlands and Ngô
- Jayce Getz (Duke University)
- Monday May 11 from 1:30 PM - 2:30 PM in BRNG 2290
- ABSTRACT: TBA
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- On the Automorphic Spectrum of Non-Quasi-Split Groups
- Tasho Kaletha (Princeton University)
- Monday May 11 from 4:30 PM - 5:30 PM in BRNG 2290
- ABSTRACT: The Langlands-Arthur conjectures provide a description of the discrete automorphic representations of connected reductive groups defined over global fields, as well as of the irreducible admissible representations of such groups defined over local fields. When the group in question is quasi-split, a precise form of these conjectures has been known for a long time and important special cases have recently been proved. For non-quasi-split groups (such as special linear, symplectic, and special orthogonal groups over division algebras), the conjectures have been vague and their proof out of reach.
In this talk we will present a precise formulation of the local and global conjectures for arbitrary connected reductive groups in characteristic zero. It is based on the construction of certain Galois gerbes defined over local and global fields and the study of their cohomology. These cohomological results place the conjectures for classical groups well within reach of the currently available methods.
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- Basic Function and Singularities in the Formal Arc Space of Reductive Monoid
- Bảo Châu Ngô (University of Chicago)
- Tuesday May 12 from 10:15 AM - 11:15 AM in BRNG 2290
- ABSTRACT: TBA
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- Trace Formula Beyond Endoscopy and Analytic Number Theory
- Salim "Ali" Altug (Columbia University)
- Tuesday May 12 from 11:30 AM - 12:30 PM in BRNG 2290
- ABSTRACT: I will talk about trace formula and analytic number theory, and how one may combine the two to get more explicit forms of the trace formula. I'll mainly discuss the elliptic part and how one can control the arithmetic issues as well as the analytic ones. I'll also discuss some applications. All this is aimed at questions motivated by beyond endoscopy.
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- Computing Basic Functions
- William Casselman (University of British Columbia)
- Tuesday May 12 from 1:45 PM - 2:45 PM in BRNG 2290
- ABSTRACT: There are formulas for p-adic basic functions due to W-W Li, Ngô, and Sakellaridis, but they don't give a very explicit idea of what they look like. It turns out to be feasible and illuminating to compute examples for groups of very low rank. I'll exhibit some, explain the difficulties in dealing with groups of high rank, and speculate about asymptotic behaviour.
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- On the Continuity of the Geometric Side of Arthur's Trace Formula
- Tobias Finis (Free University of Berlin, Germany)
- Wednesday May 13 from 9:00 AM - 10:00 AM in BRNG 2290
- ABSTRACT: I'll report on joint work with Erez Lapid that extends the methods of our 2011 Compositio paper to deal at least with the coarse geometric expansion of the (non-invariant) trace formula.
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- Questions and Remarks
- Freydoon Shahidi (Purdue University)
- Wednesday May 13 from 10:30 AM - 11:30 AM in BRNG 2290
- ABSTRACT: I plan to pose certain questions in connection with Ngô's monoid construction of L-functions as motivated by my own work on comparison of root numbers and related matters, as well as questions concerning non-vanishing of certain periods in terms of Arthur parameters and possible connections to the work of Sakellaridis-Venkatesh.
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