Microlocal theory of sheaves in symplectic geometry
(Fall 2022)

Organizers: Johan Asplund and Yash Deshmukh.

Description: The goal of this seminar is to study some basics of the microlocal theory of sheaves and its relationship with symplectic geometry. The first half of the semester will be devoted to basic definitions, some applications and also computations. The second half of the semester will consist of understanding the proof of a theorem by Ganatra–Pardon–Shende which relates the partially wrapped Fukaya category of a Weinstein manifold to a category of microlocal sheaves on its skeleton.

Time and location: Tuesdays 12:00–1:00 pm ET, Math 407.

Zoom link: https://columbiauniversity.zoom.us/j/96232308451?pwd=VmxzTjRoVGs1YjdwUlhiMGMvQ2pYUT09


Schedule (subject to change)

Note: Non-standard seminar dates or locations are marked with ※.
Date Speaker Topic Ref
Sep 27 Yash Deshmukh and Sebastian Haney Basics of microlocal sheaves I
Show/hide abstract In the next 1.5 talks, we will begin discussing the basics of microlocal sheaf theory. After recalling some facts about Whitney stratifications and the shriek functors, we will define the microsupport of a sheaf. We will also prove a result characterizing the microsupport of a constructible sheaf.
[GPS18, KS90] Notes
Oct 4 Sebastian Haney Basics of microlocal sheaves II
Show/hide abstract We continue with discussing of the basics of microlocal sheaf theory. After recalling some facts about Whitney stratifications and the shriek functors, we will define the microsupport of a sheaf. We will also prove a result characterizing the microsupport of a constructible sheaf.
[GPS18, KS90] Notes
Oct 11 Alex Xu Basics of microlocal sheaves III
Show/hide abstract We continue developing the terminology for microlocal sheaf theory. We begin by constructing the microstalk 'functor' and discuss various geometric aspects of the construction. Afterwards, we will discuss key properties, such as co-representability and their role within the category Sh_X(M). If time permits, we will attempt to place this into the broader picture of [GPS18].
[GPS18, KS90]
Oct 13 12:00 pm Math 407 Juan Muñoz-Echániz Nadler–Zaslow correspondence [NZ09]
Oct 25 Johan Asplund Legendrian knots and constructible sheaves [STZ17]
Nov 1 Yin Li Wrapped microlocal sheaves on pairs of pants [Nad16]
Nov 8 Sebastian Haney Arboreal singularities [Nad17]
Nov 15 TBA Backup
Nov 22 Yash Deshmukh Ganatra–Pardon–Shende I [GPS18]
Nov 29 Andrew Hanlon Ganatra–Pardon–Shende II [GPS18]
Dec 6 TBA Ganatra–Pardon–Shende III [GPS18]
Dec 13 TBA Ganatra–Pardon–Shende IV [GPS18]

References