Fukaya categories and mirror symmetry

Eilenberg Lectures, Fall 2016 -- Denis Auroux

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)