Kashiwara-Schapira Seminar

This page was last updated Summer 2017, when the seminar occurred (with the exception of this edit)

OVERVIEW

This seminar is about sheaf theory in microlocal analysis, with an eye towards symplectic geometry, following the perspective of Kashiwara and Schapira. The hope is to give an introduction suitable enough for the audience to begin to be able to read modern literature invoking these techniques in symplectic geometry (see the reference list below). We will begin by understanding first the language of derived categories, and necessary background on sheaves, following Chapters I-II of [KS]. We will then work through the notes [Sc], understanding singular support as well as some applications to non-displaceability in symplectic geometry and PDEs. Finally, should time permit, we will continue on with some subset of the other resources listed below, encountering various applications of the theory to symplectic geometry.

We meet Thursdays 11-12:30 in Room 2-361 (at MIT).

NOTES

• Derived categories and derived functors, notes and talk by Melissa Zhang
• Sheaves, six functors, definitions, and examples, notes and talk by Peter Haine
• Non-characteristic deformation lemma, notes and talk by Jianfeng Lin
• Singular support, notes and talk by Kevin Sackel

REFERENCES

• [G1] Guillermou. The Gromov-Eliashberg theorem by microlocal sheaf theory
• [G2] Guillermou. The three cusps conjecture
• [GKS] Guillermou-Kashiwara-Schapira. Sheaf quantization of Hamiltonian isotopies and applications to non displaceability problems
• [GS] Guillermou-Schapira. Microlocal theory of sheaves and Tamarkin's non displaceability theorem
• [JT] Jin-Treumann. Brane structures in microlocal sheaf theory
• [KS] Kashiwara-Schapira. Sheaves on Manifolds
• [N1] Nadler. Wrapped microlocal sheaves on pairs of pants
• [N2] Nadler. Arboreal singularities
• [NZ] Nadler-Zaslow. Constructible sheaves and the Fukaya Category
• [Sc] Schapira. A short review of microlocal sheaf theory
• [Sh] Shende. The conormal torus is a complete knot invariant
• [TZ] Treumann-Zaslow. Cubic planar graphs and Legendrian surface theory

Organizers

Kevin Sackel, Melissa Zhang