Math 226B:  Fukaya Categories
Fall 2023


Fukaya categories occupy a central role in modern mathematics, at the junction of algebraic geometry, symplectic geometry, low-dimensional topology, and mathematical physics.  The goal of this course is to give an introduction to Lagrangian Floer homology, Fukaya categories, and homological mirror symmetry.

Instructor: Ko Honda
Office Hours: Mondays 2:30-3:30pm or by appointment
E-mail: honda at math dot ucla dot edu

Class Meetings:  Lectures are MWF 10-10:50am at MS 5203.

  1. Some symplectic geometry
  2. Lagrangian Floer (co-)homology
  3. A-infinity algebras and A-infinity categories
  4. Construction of the Fukaya categories and some variants including the wrapped Fukaya category
  5. Exact triangles, twists, split generation
  6. Homological mirror symmetry e.g. of the torus
Prerequisites: Math 225 sequence or equivalent (a good knowledge of differentiable manifolds and homology).  Some knowledge of symplectic geometry is helpful, but not necessary.

Grading: TBA


Basics of symplectic geometry:
  1. D. McDuff and D. Salamon, Introduction to symplectic topology, 2nd edition, Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York, 1998.
  2. A. Cannas da Silva, Lectures on symplectic geometry.
A-infinity algebras:
  1. B. Keller, Introduction to A-infinity algebras and modules.

Fukaya categories:

  1. D. Auroux, A beginner's introduction to Fukaya categories.
  2. P. Seidel, Fukaya categories and Picard-Lefschetz theory.

WARNING:  The course syllabus provides a general plan for the course; deviations may become necessary.
Last modified: September 20, 2023.