Derived Algebraic Geometry Student Seminar Fall 2024
The topic for the semester is singular support of (ind-)coherent sheaves and matrix factorizations. Some references are Arinkin-Gaitsgory 1, Arinkin-Gaitsgory 2, Beraldo-Lin-Reeves, and di Fiore’s thesis. We are currently meeting in Evans 891 Tuesdays 9-11.
If you’d like to join remotely, send me an e-mail so that I open Zoom. Here’s the Zoom link.
| Date | Speaker | Title | Abstract | Notes |
|---|---|---|---|---|
| 2/11 | Swapnil Garg | Singular Support of Constructible Sheaves | I will review singular support of constructible sheaves and D-modules, in particular highlighting the construction of the sheaf of categories over \(T^*X\) called \(\mu Sh_\Lambda\), for \(\Lambda\) a conical Lagrangian in \(T^*X\). If time permits, I will then explain the concept of the singular support of a strong \(G\)-category \(C\) (i.e. a \(D(G)\)-module \(C\)), which is a subset of \(Lie(G)^*\), following Dhillon–Faergeman. | |
| 2/18 | Ansuman Bardalai | Singular Support of Coherent Sheaves I | I will try to define the notion of singular support of coherent sheaves (with some motivation). | |
| 2/25 | Yuji Okitani | Singular Support of Coherent Sheaves II | I will discuss several methods to compute singular support of coherent sheaves. I will also try to outline the conceptual definition of singular support, following David’s GRT talk from last year. | |
| 3/3 | Yuji Okitani | Singular Support of Coherent Sheaves III | Continuation of previous week’s talk. | |
| 3/31 | Jacob Erlikhman | IndCoh as a Crystal of Categories I | I will try to explain how IndCoh(X) forms a crystal of categories on Sing(X) via the assignment N \mapsto IndCoh_N(X). More precisely, I’ll focus on the (big) category of singularities IndCoh(X)/QCoh(X) as a crystal of categories on the projectivization PSing(X). | |
| 4/7 | Jacob Erlikhman | IndCoh as a Crystal of Categories II | Continuation of previous week’s talk. |