Math 253y - Symplectic Manifolds and Lagrangian Submanifolds - Fall 2018

D. Auroux - Tue. & Thu., 10:30-11:45am, Science Center 222

Instructor: Denis Auroux (

Office: Science Center 539.
Office hours: Tuesdays 12-1 and Thursdays 9-10 (subject to change).
Course assistant: Yu-Wei Fan (ywfan@math), office hours Wednesdays 1:30-3 in SC 310.



There will be 3-4 homework assignments during the semester, including a more substantial assignment at the end of the semester serving as take-home final assessment.

Material covered

Lecture notes

These handwritten notes may be incomplete or incorrect -- use at your own risk.

Course outline

The course will start with a review of standard symplectic topology: symplectic manifolds, Lagrangian submanifolds, neighborhood theorems, almost-complex structures and compatibility, Hamiltonian group actions. The focus will then shift towards J-holomorphic curves: moduli spaces, Gromov compactness, etc., with a view towards Lagrangian Floer theory. The final part of the course will give a taste of more advanced topics: invariants of monotone Lagrangians; Fukaya categories; mirror symmetry.

Provisional list of topics (to be adjusted):

Prerequisites: a solid knowledge of differential geometry, and basic algebraic topology (Math 230a and Math 231a).

Reference books

Basic symplectic geometry:

J-holomorphic curves:

Floer homology and Fukaya categories: