Plan of Talks

This is an outline of the schedule of talks at the workshop.

Update 5/25: An expanded syllabus is now online. It contains detailed descriptions of what each talk ought to cover, as well as a summary of goals for the workshop. Please have a look!

Day 1: Monday 6/13

Singularities and constructible sheaves
  1. Overview of week. Nick's notes
  2. (Ian Shipman) Tame geometry. Subanalytic geometry. Defining functions. Stratifications and triangulations. Thom isotopy lemmas. Example of real line. Refs: [BM88], [VM96] Nick's notes
  3. (Hiro Tanaka) Homotopical categories. Differential graded and A∞ -categories. Functors and modules. Linear structure: shifts and cones. Localization with respect to collection of morphisms. Homological perturbation theory. Refs: [Ke06], [S], [L] Nick's notes
  4. (Justin Curry) Constructible sheaves. Differential graded category of sheaves. Functoriality under maps. Standard triangles and bases. Relation to constructible functions. Refs: [KS84], [GM83] Nick's notes
  5. (Daniel Rowe) Examples. Constructible sheaves on S^1 stratified with a single marked point. Constructible sheaves on A^1 stratified with a single marked point. Constructible sheaves on Schubert stratifications. Nick's notes

Day 2: Tuesday 6/14

Microlocal geometry of sheaves
  1. (Aliakbar Daemi) Cotangent bundles. Exact symplectic structure. Geodesic flow. Examples of Lagrangians: conormals, graphs and generalizations. Conormals to stratification. Con- ical Lagrangian cycles. Refs: [A], [KS84] Nick's notes
  2. (Thomas Bitoun) Characteristic cycles. From constructible sheaves to conical Lagrangian cycles. Functoriality under maps. Refs: [KS84], [SV96] Nick's notes
  3. (Faisal Al-Faisal) Intersection of Lagrangian cycles. Perturbations near infinity. Gradings. In- tersections of characteristic cycles: index theorems, compatibility with multiplication of constructible functions. Refs: [GrM97], [NZ09] Nick's notes
  4. (Sarah Kitchen) Riemann-Hilbert correspondence. Differential operators as quantization of functions on cotangent bundle. Algebraic model of constructible sheaves: regular holo- nomic D-modules. Refs: [Be], [Kap] Nick's notes
  5. Discussion Nick's notes

Day 3: Wednesday 6/15

Exact Lagrangians in cotangent bundles
  1. Overview Nick's notes
  2. (Agnes Gadbled) Exact Floer-Fukaya theory. Fukaya category of compact exact Lagrangians in exact symplectic target. Brane structures. Moduli spaces of disks. Organization into A∞ -category. Refs: [S] Nick's notes
  3. (Thomas Kragh) Morse category of submanifolds. Gradient tree A∞ -category of submanifolds with local systems. Equivalence with constructible sheaves. Refs: [KS01], [NZ09] Nick's notes
  4. (Toly Preygel) Infinitesimal Fukaya category of cotangent bundle. Noncompact branes: perturbations, taming, bounds on disks. Comparisons with directed and wrapped Fukaya categories. Equivalence of subcategory of standard branes with Morse cate- gory of submanifolds. Refs: [S], [Sik94], [FO97], [NZ09], [Nspr] Nick's notes
  5. (Dario Beraldo) Equivalence of sheaves and branes. Formalism of Yoneda lemma and bimod- ules. Beilinson’s argument. Decomposition of diagonal. Noncharacteristic motions. Refs: [B78], [N09], [Nspr] Nick's notes

Day 4: Thursday 6/16

Some examples and applications
  1. (James Pascaleff) Mirror symmetry for toric varieties. Fukaya category of cotangent bundle of torus. Refs: [FLTZ] and related papers. Nick's notes
  2. (Nick Rozenblyum) Springer theory. Fukaya category of cotangent bundle of Lie algebra. Fourier transform from Floer perspective. Refs: [BoM81], [Nspr] Nick's notes
  3. (Travis Schedler) Microlocalization and Hamiltonian reduction. Formalism of microlocaliza- tion and Hamiltonian reduction. Introduction to crepant resolutions and their quanti- zations. Nick's notes
  4. (Chris Dodd and Sheel Ganatra) W-algebras from topological viewpoint. Fukaya category beyond compact branes in Slodowy slices. Refs: [KhS], [SS], [Ma], [Lo] among many related papers. Nick's notes on Chris' talk, Nick's notes on Sheel's talk

Day 5: Friday 6/17

Further directions
  1. (David Nadler) Gauge theory setting. Hitchin integrable system. Relation to talks of previous day. Challenge of quantization of fibers. Refs: [BD], [KW], [Kap]
  2. (David Nadler) Where to go from here. Nick's notes (incomplete)