Tropical Fukaya Algebras

We will meet on Wednesdays from 1:30PM to 3:00PM at CMSA room G02, for a 1 hour talk followed by a 30 minute discussion session. 

The goal of this reading seminar is to understand tropical Fukaya algebras defined in the work of Venugopalan-Woodward. The tentative topics are listed below.

Please feel free to ask questions to the organizers Yonghwan Kim (yonghkim@mit.edu) and Sebastian Haney (haney@math.harvard.edu).

Schedule

Week 1 (Sep 16) 2:15pm, SC304 Overview (Yonghwan Kim) [VW25, Chapter 1] Notes

Week 2 (Sep 23) Examples (Denis Auroux) [VW25, Chapter 2]

CMSA Lagrangian Floer theory and applications workshop

Week 3 (Oct 7) Fukaya algebras (Donghae Lee) [CW22, Chapter 4]

Week 4 (Oct 14) Stabilizing divisors - constructions and perturbation schemes (Roman Krutowski) [VW25, Chapters 5, 6] [CM07]

Week 5 (Oct 21) Broken manifolds (Jiarui Wen) [VW25, Chapter 3], [Lerman95]

Week 6 (Oct 28) Broken Fukaya algebras, and overview of the paper (Sebastian Haney) [VW25, Chapter 10]

Week 7 (Nov 4) Applications to almost toric fibrations, del Pezzo surfaces (Samuel Sottile) [VW26], [Woodward26]

Week 8 (Nov 9) Outlook (Chris Woodward)

Week 9 (Nov 16) Interactions between quantum and homotopical geometry workshop, Simons center

CMSA Lagrangian Floer theory and applications program ends

Suggested references

Auroux - A remark about Donaldson's construction of symplectic submanifolds (arXiv link)

Charest, Woodward 15 - Fukaya algebras via stabilizing divisors (arXiv link)

Charest, Woodward 22 - Floer cohomology and flips (arXiv link)

Cieliebak, Mohnke 07 - Symplectic hypersurfaces and transversality in Gromov-Witten theory (arXiv link)

Donaldson 96 -  Symplectic submanifolds and almost-complex geometry (journal link)

Hoek 25 - A Morse-theoretic approach to family Floer homology (thesis link)

Jing 25 - On SYZ mirrors of Hirzebruch surfaces (arXiv link)

Lerman 95 - Symplectic cuts (journal link)

Pascaleff, Tonkonog 20 - The wall-crossing formula and Lagrangian mutations (arXiv link)

Venugopalan, Woodward, Xu 25 - Fukaya categories of blowups (arXiv link)

Venugopalan, Woodward 25 - Tropical Fukaya algebras (arXiv link)

Venugopalan, Woodward 25b - Splitting the diagonal for broken maps (arXiv link)

Venugopalan, Woodward 26 - Tropical disc potentials for almost toric manifolds (arXiv link)

Woodward 26 - Holomorphic disks and tropical Lagrangians (arXiv link)