The course will be divided into three parts:
preliminary in symplectic geometry and Floer theory
mirror symmetry
Picard-Lefschetz theory


  1. moduli space of curves
  2. stable compactification
  3. Gromov-Witten theory
  4. A structures and A homomorphisms
  5. homotopy perturbation lemma
  6. Lagrangian Floer homology
  7. Fukaya cateogry
Mirror symmetry/enumerative geometry:
  1. Strominger-Yau-Zaslow conjecture
  2. twisted complexes and the derived category of an A category
  3. homological mirror symmetry
  4. SYZ transformation
  5. mirror symmetry of elliptic curves
  6. Landau-Ginzburg models and superpotentials
  7. Family Floer homology
  8. tropical geometry
  9. correspondence theorem
Picard-Lefschetz Theory:
  1. Fukaya-Seidel category
  2. vanishing cycles and matching cycles
  3. Lagrangian surgery and Mapping Cones
  4. A_n Milnor fibres
  5. HMS of del Pezzo surface,
  6. Picard-Lefschetz theorem 2 1/2