This is an informal symplectic reading group on Local to Global Principles in Symplectic Topology during Spring 2022. Our tentative goal is to read the first two (and the third, if time permits) of a series of papers by Ganatra, Pardon and Shende on Fukaya categories of Liouville sectors and their local to global properties. Depending on everyone's interest, possible topics towards the end may also include sheaf theoretic methods in symplectic topology, comparison with the GPS approach, and some application to mirror symmetry, etc.
The reading group will meet weekly on Monday, 4:15-5:15pm in MIT 2-255 (Building 2, Room 255). Our first meeting will be Jan 31st, and we'll have an overview of the potential topics.
Schedule
Jan 31 Organizational meeting/Overview
Feb 7 (Jiakai) Basics on homogeneous symplectic geometry and contact geometry (Liouville, contact geometry)
Feb 14 (Zihong) Digression: Open-closed, Closed-open maps, Abouzaid's generation
Feb 21 (Clair) Liouville Sectors (definitions, comparison with other notions (e.g. stops), examples); GPS1, 2.1-2.8
Feb 28 (Jaewon) Floer theory of sectors (maximum principle, example computations) ; GPS1, 2.9, 3.2-3.5
Mar 7 (Jae) Covariant functoriality of WFuk under sector inclusions; GPS1, 3.8-3.9
Mar 14 Spring Break
Mar 21 (Zihong) Infinity-categories of Floer data, symplectic cohomology and open-closed map for Liouville sectors; GPS1, Chapter 4
Mar 28 (Maxim) Weinstein manifolds (Definitions, examples, Lagrangian cores, Wein functor)
Apr 4 Break due to Miami conference
Apr 11 (Jae) Working with Fukaya category (The wrapping exact sequence, linking discs, example computations); GPS2, Chapter 3 & 4
Apr 18 (Clair) Stop removal functors, example computations; GPS2, Chapter 5
Apr 25 (Jaewon) More structual properties and computations (Künneth, stablizations, with examples); GPS2, Chapter 6
May 2 (Zihong) (co)descent and computations; GPS2, Chapter 9
May 9 (Jae) Application: Generation by cocores (behavior of cocores/linking discs under operations, ...); GPS2, Chapter 7
Main reference:
Ganatra, Pardon, Shende, Covariantly functorial wrapped Floer theory on Liouville sectors, arxiv.org/abs/1706.03152v3
Ganatra, Pardon, Shende, Sectorial descent for wrapped Fukaya categories, arxiv.org/abs/1809.03427
Ganatra, Pardon, Shende, Microlocal Morse Theory Of Wrapped Fukaya Categories, arxiv.org/abs/1809.03427
Other useful sources:
M. Abouzaid, A geometric criterion for generating Fukaya categories, arxiv.org/abs/1001.4593
Y. Eliashberg, Weinstein manifolds revisited, arxiv.org/abs/1707.03442
S. Ganatra, Symplectic cohomology and duality for the wrapped Fukaya category, arxiv.org/abs/1304.7312