Math 257A

Introduction to Symplectic Geometry

(MWF 9:30-10:20 @ 200-303)

Office hours: W, 4-5pm

Grades and homework:

Bi-weekly homeworks will be posted here. Grade is entirely based on homework.

Problem set 1 (due Oct 4)  Solution to q4 (by Dylan)

Problem set 2 (due Oct 18)

Plan for the course:

- The first 8 lectures of "Lectures on Symplectic Manifolds", by Alan Weinstein

- Gromov non-squeezing theorem (possibly from Gromov's original paper, cited below)

- Symplectic rigidity of Lagrangian submanifolds (from Audin-Lalonde-Polterovich article cited below)

Schedule

Week 1: Lecture 1 and the proposition at the last page of Lecture 8 (W)

Week 2: Lecture 2 (will not talk about polarizations except the totally complex ones)

Week 3: Complex manifolds, Stein manifolds, Kahler manifolds, Fubini-Study form on CP^n

Week 4: Non-Kahler closed symplectic manifolds, symplectic reduction, Hamiltonian vector fields

Sources 

Weinstein, Lectures on Symplectic Manifolds (book)

Gromov, Pseudo-holomorphic curves in symplectic manifolds

Audin-Lalonde-Polterovich, Symplectic rigidity: Lagrangian submanifolds

---Some other books on basic symplectic geometry (not required)

McDuff-Salamon, Introduction to Symplectic Topology 

Da Silva, Lectures on Symplectic Geometry

Arnol'd, Mathematical Methods of Classical Mechanics

 

 

Last modified Sun, 13 Oct, 2019 at 21:01