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
Mirror symmetry/enumerative geometry:
- 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
Picard-Lefschetz Theory:
- 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