The course will be divided into three parts:

preliminary in symplectic geometry and Floer theory

mirror symmetry

Picard-Lefschetz theory

Preliminary

- moduli space of curves
- stable compactification
- Gromov-Witten theory
- A
_{∞}structures and A_{∞}homomorphisms - homotopy perturbation lemma
- Lagrangian Floer homology
- Fukaya cateogry

- Strominger-Yau-Zaslow conjecture
- twisted complexes and the derived category of an A
_{∞}category - homological mirror symmetry
- SYZ transformation
- mirror symmetry of elliptic curves
- Landau-Ginzburg models and superpotentials
- Family Floer homology
- tropical geometry
- correspondence theorem

- Fukaya-Seidel category
- vanishing cycles and matching cycles
- Lagrangian surgery and Mapping Cones
- A_n Milnor fibres
- HMS of del Pezzo surface,
- Picard-Lefschetz theorem 2 1/2