P-adic Arthur Packets Seminar - Spring 2024

In Adams, Barbasch and Vogan's book on the local Langlands correspondence for real groups, the authors introduced a geometric construction of local Arthur packets using perverse sheaves and microlocal analysis. A similar geometrization was recently formulated by Cunningham et. al. for p-adic groups providing a unified framework to work with Arthur packets.

In this reading seminar we will work through the two papers "Arthur packets for p-adic groups by way of microlocal vanishing cycles of perverse sheaves with examples" (2017) and "Arthur packets for G2 and perverse sheaves on cubics" (2020).

Time and Venue

Time: 1-3pm, Wednesdays

Venue: S17-0406, except on Feb 7, and March 27, when it is S17-0511

Schedule

• Lecture 1 (Feb 7, S17-0511) - Overview
  Speaker: Emile
• Lecture 2 (Feb 14, S17-0406) - The geometrization of the space of L and A-parameters
  Speaker: Emile
• Lecture 3 (Feb 21, S17-0406) - Microlocal vanishing cycles of perverse sheaves I
  Speaker: Dave
• (No lecture Feb 28)
• Lecture 4 (Mar 6, S17-0406) - Microlocal vanishing cycles of perverse sheaves II
  Speaker: Bryan
• Lecture 5 (Mar 13, S17-0406) - ABV Arthur packets
  Speaker: Argo
• Lecture 6 (Mar 20, S17-0406) - Moduli space of homogeneous cubics
  Speaker: York
• Lecture 7 (Mar 27, S17-0511) - Subregular Arthur packets for G2
  Speaker: Hoang
• Lecture 8 (Apr 3, S17-0406) - Proof of Vogan's conjecture for GLn
  Speaker: Yi
• Lecture 9 (Apr 10, S17-0406) - ABV packets attached to non-Arthur L-parameters
  Speaker: Argo
• Lecture 10 (Apr 17, S17-0406) - Perverse sheaves, quivers, and quantum groups
  Speaker: Ed

References

• [M] L. Maxim, Notes on vanishing cycles and applications
• [BCHM] D. Ben-Zvi, H. Chen, D. Helm, D. Nadler, Between Coherent and Constructible Local Langlands Correspondences
• [CFK] C. Cunningham, A. Fiori, N. Kitt, Appearance of the Kashiwara-Saito singularity in the representation theory of p-adic GL16
• [CFMMX] C. Cunningham, A. Fiori, A, Moussaoui, J. Mracek, B. Xu, Arthur packets for p-adic groups by way of microlocal vanishing cycles of perverse sheaves with examples
• [CR1] C. Cunningham, M. Ray, Proof of Vogan's conjecture on Arthur packets: irreducible parameters of p-adic general linear groups
• [CR2] C. Cunningham, M. Ray, Proof of Vogan's conjecture on Arthur packets for GLn over p-adic fields
• [CFZ] C. Cunningham, A. Fiori, Q. Zhang, Arthur packets for G2 and perverse sheaves on cubics