Working group on Zhu's tame categorical local Langlands correspondence

The goal of this working group is to study the paper "Tame categorical local Langlands correspondence" by X. Zhu.

Participants

Alexandre Démoulin (Université Clermont Auvergne)
Gabriel Dospinescu (CNRS, Université Clermont Auvergne)
Simon Riche (Université Clermont Auvergne)
Benjamin Schraen (Université Claude Bernard Lyon 1)
Quan Situ (Université Clermont Auvergne)

Schedule

May 22nd, 2026: Chapters 8-9-10.
May 29th, 2026: Chapters 7-10.
June 5th, 2026: Chapters 8-9-10.
June 16th, 2026: Chapter 3.
June 19th, 2026: Chapter 3.
June 25th, 2026: Chapters 2-3-4.
June 30th, 2026: Chapter 4.
July 1st, 2026: Chapter 4.
July 3rd, 2026: Chapters 2-4.

Notes

Notes for the talks:

May 22nd, 2026:

Talk 1 (G. Dospinescu): Sheaf theories (§§8.1-8.2). Constructible sheaves on perfect schemes (§§10.1-10.2).
Talk 2 (Q. Situ): Derived algebraic geometry (§9.1). Quasi-coherent sheaves (§9.2).
Talk 3 (A. Démoulin): Ind-coherent sheaves and *-functors (§§9.3.1-9.3.2).
Talk 4 (S. Riche): !-pullback for Ind-coherent sheaves (§9.3.3) and Grothendieck-Serre duality (§9.3.4).

May 29th, 2026:

Talk 1 (G. Dospinescu): More on constructible sheaves on perfect (pre)stacks (§§10.3-10.4-10.5).
Talk 2 (S. Riche): Dualizability and admissibility (§7.2).
Talk 3 (A. Démoulin): Trace and center (§§7.2-7.3).

June 5th, 2026:

Talk 1 (G. Dospinescu): Even more on constructible sheaves on perfect (pre)stacks (§10.6).
Talk 2 (S. Riche): Singular support of coherent sheaves (§9.4).
Talk 3 (Q. Situ): Geometric traces in sheaf theory (§8.3).

June 16th, 2026:

Talk 1 (B. Schraen): Shtukas and isocrystals (§§3.1-3.2).

June 19th, 2026:

Talk 1 (G. Dospinescu): Sheaves on classifying stacks of locally profinite groups and isocrystals (§§3.3-3.4).

June 25th, 2026:

Talk 1 (G. Dospinescu): More on the local Langlands category (§3.4). The stack of local Langlands parameters (§§2.1-2.2).
Talk 2 (S. Riche): Affine Hecke categories (§4.2). Affine Deligne-Lusztig theory (§4.3).

June 31st, 2026:

Talk 1 (A. Démoulin): Monodromic sheaves (§4.1).

July 1st, 2026:

Talk 1 (S. Riche): Deligne-Lusztig theory (§§4.3-4.4).

July 3rd, 2026:

Talk 1 (G. Dospinescu): Computation of trace on the coherent side (§2.3).
Talk 2 (Q. Situ): Computation of trace on the constructible side (§4.5).

Any comments on these notes are welcome!

Funding

This research is funded by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 101002592)◊.