Institute for Mathematical Sciences

On the Langlands Program: Endoscopy and Beyond

(17 Dec 2018 - 18 Jan 2019)



General Enquiries: ims(AT)nus.edu.sg
Scientific Aspects Enquiries: matzhlei(AT)nus.edu.sg

This programme will focus on the study of the Langlands functoriality conjecture, including the endoscopy theory and the cases beyond endoscopy.

For the endoscopy case, Langlands functoriality is established by using the trace formula approach in general. Some special cases can also be established by the converse theorem-integral representation approach, and the automorphic integral transform approach.

Based on those successful cases, several new approaches are proposed. The key idea is to construct certain appropriate automorphic kernel functions and study them in various ways in order to establish functorial transfers for automorphic forms in the relative general setting.

These bring us the following four topics of the program:
  • Refined structures and properties for endoscopy theory: local and global.
  • Various types of trace formulas, generalized Fourier transforms and Poisson summation formulas, and applications.
  • Explicit constructions of certain Langlands functorial transfers via integral transformations.
  • Extension of the existing theory in the Langlands program to covering groups.
The goal of the program is to bring together experts researching in automorphic kernel functions to foster interaction, collaboration and the exchange of ideas on the new approaches. It aims to develop those approaches that will provide us further insights and progress, and lead to an eventual resolution of the Langlands functoriality conjectures.

  • Week 1 (17-21 December 2018)
    • Introductory Courses on Arthur Packets
      Hiraku Atobe, Kyoto University and Wee Teck Gan, National University of Singapore
    • Introductory Courses on The Approach of Braverman-Kazhdan-Ngo to L-Functions
      Lei Zhang, National University of Singapore
    • Introductory Courses on The Stable Trace Formula, with Emphasis on SL(2)
      Abhishek Parab, Purdue University
  • Week 2 (26-28 December 2018)
    • Introductory Courses on The Approach of Braverman-Kazhdan-Ngo to L-Functions
      Zhilin (Ray) Luo, University of Minnesota
    • Introductory Courses on The Stable Trace Formula, with Emphasis on SL(2)
      Tasho Kaletha, University of Michigan
    • Introductory Courses on The Approach of Altug and Arthur Regarding Beyond Endoscopy
      Julia Gordon, The University of British Columbia
  • Week 3 (2-4 January 2019)
    • Introductory Courses on The Approach of Braverman-Kazhdan-Ngo to L-Functions
      Zhilin (Ray) Luo, University of Minnesota
    • Introductory Courses on The Stable Trace Formula, with Emphasis on SL(2)
      Tasho Kaletha, University of Michigan
    • Introductory Courses on The Approach of Altug and Arthur Regarding Beyond Endoscopy
      Ali Altuğ, Boston University and Julia Gordon, The University of British Columbia
  • Week 4 (7-11 January 2019)
    • Research Conference
    • IMS Distinguished Visitor Lecture Series Part (1) by Ngô Bảo Châu, The University of Chicago, USA and Vietnam Institute for Advanced Study in Mathematics, Vietnam
  • Week 5 (14-18 January 2019)

  • Please note that our office will be closed on the following public holiday.
    - 25 Dec 2018, Christmas day.
    - 1 Jan 2019, New Year's day.


    Venue:

Registration Closed.


Group photo will be uploaded at a later date.