Toric FOOO learning seminar - Spring 2020

Goal is to understand the use of toric degeneration and bulk deformation in the study of nondisplacability of Lagrangian tori.

References:

Intro to Lagrangian Floer:

  • Auroux, A beginner's introduction to Fukaya category

  • Smith, A symplectic prolegomenon

  • Pascaleff's lecture notes

Toric FOOO:

  • [TFOOO1] Lagrangian Floer theory on compact toric manifolds I

  • [TFOOO2] Lagrangian Floer theory on compact toric manifolds II: bulk deformation

  • [TFOOO survey] Lagrangian Floer theory on compact toric manifolds: survey

  • [big FOOO1] Lagrangian Intersection Floer Theory: Anomaly and Obstruction, Part I

  • [Ohta] Obstruction to and Deformation of Lagrangian intersection floer cohomology

Application to Lagrangian tori:

  • [toric degeneration] Toric degeneration and non-displaceable Lagrangian tori in S2×S2

  • [Wu] On an exotic Lagrangian torus in CP2

  • [Mak-Smith] Non-displaceable Lagrangian links in four-manifolds

  • [Sun] An-type surface singularity and nondisplaceable Lagrangian tori

Schedule:

  • 4-25 Jie Min Intro to Lagrangian Floer cohomology 1

  • 5-2 Jie Min Intro to Lagrangian Floer cohomology 2

  • 5-9 Shuo Zhang Gromov compactness and bubbling

  • 5-16 Liya Ouyang A_\infty algebra and deformation.
    Jie Min Canonical model

  • 5-23 Shengzhen Ning Toric manifolds

  • 5-30 Jie Min Calculation of potential function

  • 6-6 Jie Min Toric degeneration and gluing