**Time and place: **Thursdays, 1.10pm-2:25pm, in Math 520.

Date |
Topics |
Video link |
Lecture notes |

09/08 | Overview: Floer theory, Fukaya categories, HMS | Lecture 1 | Jo, Luis (missing start) |

09/15 | Lagrangian Floer cohomology: definition, d^2 = 0 | Lecture 2 | Luis, Jo |

09/22 | Lagrangian Floer cohomology: invariance, grading, HF(L,L) | Lecture 3 | Luis |

09/29 |
Products and A_{∞} structure |
Lecture 4 | Luis, Jo |

10/06 | Fukaya category; examples: cylinder and T^2 | Lecture 5 | Luis |

10/13 | Twisted complexes; split-generators for T^2; introduction to wrapped Floer theory | Lecture 6 | Luis |

10/20 | Wrapped Fukaya category; HMS for the cylinder; FS(C*, z+1/z) and HMS for CP^1. | Lecture 7 | Luis |

10/27 | Compactification, deformation and superpotentials; m_0 obstruction; example: CP^1. | Lecture 8 | Luis |

11/03 | Recap: LG models, Fukaya-Seidel category, matrix factorizations, and HMS for toric Fanos. | Lecture 9 | Luis |

11/10 | No lecture: HMS workshop at the IAS | ||

11/17 | The pair of pants. | Lecture 10 (no sound) | Luis |

11/24 | Thanksgiving -- no lecture | ||

12/01 | Towards HMS for higher dimensional pants, hypersurfaces in (C*)^n and their complements. | Lecture 11 | Luis |

12/08 | Fukaya categories of toric LG models, HMS for hypersurfaces in (C*)^n and toric varieties. | Lecture 12 | Luis |

You can also watch the videos as a YouTube playlist

**Further resources: **

Auroux, A beginners' introduction to Fukaya categories

Sheridan, Notes from a mini-course on the Fukaya category (Jussieu, summer 2016)

Auroux, Notes from a topics course on HMS (2009, Berkeley)