(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

Date | Speaker | Topic | Ref |
---|---|---|---|

Sep 27^{※} |
Yash Deshmukh and Sebastian Haney | Basics of microlocal sheaves I
## Show/hide abstractIn 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 abstractWe 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 abstractWe 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] |

- [GPS18] S. Ganatra, J. Pardon, and V. Shende.
**Microlocal Morse theory of wrapped Fukaya categories**, (2018). [arxiv:1809.08807] - [KS90] M. Kashiwara and P. Schapira.
**Sheaves on manifolds**, Springer-Verlag, Berlin (1990). - [Nad16] D. Nadler.
**Wrapped microlocal sheaves on pairs of pants**, (2016). [arxiv:1604.00114] - [Nad17] D. Nadler.
**Arboreal singularities**, Geom. Topol., 21 (2017). [arxiv:1309.4122] - [NZ09] D. Nadler and E. Zaslow.
**Constructible sheaves and the Fukaya category**, J. Amer. Math. Soc., 22 (2009). [arxiv:0604379] - [STZ17] V. Shende, D. Treumann, and E. Zaslow.
**Legendrian knots and constructible sheaves**, Invent. Math., 207 (2017). [arxiv:1402.0490]