Adeel A. Khan

Étale microlocalization seminar

Institute of Mathematics, Academia Sinica • Fall 2026

Time and place

Seminar Room 638, 6F, Astronomy-Mathematics Building, NTU Campus
Thursdays 13:00 – 15:00
October 1st – December 24th, 2026

Organizers

Ping-Hsun Chuang, Adeel Khan

Description

A reading seminar on singular support and microlocalization in the context of étale sheaves, following the work of Beilinson, Saito, Xiong–Yang and others.

Program

PDF
9/16
Overview and organizational meeting [Adeel]
10/1
1. Sheaves and local systems [Ching-En]
10/8
2. The six operations and constructible sheaves [Hung-Chun]
10/15
3. Nearby and vanishing cycles; universal local acyclicity [Andy]
10/22
4. Singular support [TBA]
This week may move to Monday or Tuesday, due to an organizer's travel plans.
10/29
5. Radon and Legendre transforms [TBA]
11/5
6. Specialization to the normal bundle [TBA]
11/12
7. The Fourier–Deligne transform [TBA]
11/19 No meeting.
11/26
8. μHom and SSμ [TBA]
12/3
9. SSμ(F) ⊆ SS(F) [TBA]
12/10 No meeting.
12/17
10. Support estimate for the microlocalization [TBA]
12/24
11. SS(F) ⊆ SSμ(F) [TBA]

References

Sheaves

  • [KS] M. Kashiwara and P. Schapira, Sheaves on manifolds, Grundlehren der mathematischen Wissenschaften 292, Springer, 1990.
  • [Kha] A. A. Khan, Constructible sheaves and vanishing cycles, lecture notes, 2025. [PDF]
  • [SGA4] M. Artin, A. Grothendieck, and J.-L. Verdier (eds.), Théorie des topos et cohomologie étale des schémas (SGA 4), tome 3, Lecture Notes in Mathematics 305, Springer, 1973.
  • [SGA4½] P. Deligne, Cohomologie étale (SGA 4½), Lecture Notes in Mathematics 569, Springer, 1977.

Vanishing cycles and local acyclicity

  • [SGA7] P. Deligne and N. Katz (eds.), Groupes de monodromie en géométrie algébrique (SGA 7 II), Lecture Notes in Mathematics 340, Springer, 1973.
  • [LZ] Q. Lu and W. Zheng, Categorical traces and a relative Lefschetz–Verdier formula, Forum Math. Sigma 10 (2022), e10. [arXiv]

Singular support and microlocalization

  • [Bei] A. Beilinson, Constructible sheaves are holonomic, Selecta Math. (N.S.) 22 (2016), 1797–1819. [arXiv]
  • [Sai] T. Saito, Characteristic cycles of constructible sheaves and microlocalization, 2026. [arXiv]
  • [XY] J. Xiong and E. Yang, Microlocalization and singular supports of constructible étale sheaves, 2026. [arXiv]