Reading Course in Symplectic Geometry

Syllabus & Textbooks

The syllabus of the course.

We will mostly follow Ana Cannas da Silva's notes. Other useful resources include Eckhard Meinrenken's notes, and Lisa Jeffrey's 2016 course.

Links to useful introductory articles about the history and philosophy of symplectic geometry.

Holm, Tara. "What is Symplectic Geometry?" Notices of the AMS 63, no. 11 (2016): 1252-1254.
Weinstein, Alan. "Symplectic geometry." Bulletin of the American mathematical society 5, no. 1 (1981): 1-13.
McDuff, Dusa. "What is Symplectic Geometry?" European Women In Mathematics. (2010): 33-53.

(Jan. 15-Jan. 29)

Jordan Hofmann's notes and homework (due January 22nd).

Brian Tran's notes and homework (due January 31st) on the symplectic linear group and Maslov index.

(Jan. 29-Feb .12)

My notes and homework (due Feb. 21st) on differential topology.

Bryce Wu's notes and homework (due Feb. 26th) on Riemannian geometry.

(Feb. 12-Feb. 26)

Jordan Hofmann's notes and homework (due March 7th) on symplectic manifolds and compatible structures.

Adriano Pacifico's notes and homework (due April 2nd) on special submanifolds of symplectic manifolds (typed version forthcoming).

(Feb. 26-Mar. 12)

Bryce Wu's notes and homework (due April 2nd) on Moser's trick and related theorems.

My notes and homework (due April 2nd) on Weinstein's tubular neighbourhood theorem and applications.

(Mar. 12-Mar.26)

Adriano Pacifico's notes and homework (due April 2nd) on complex geometry and Dolbeault cohomology (typed).

Peter Angelino's notes and homework (due April 2nd) on Kähler manifolds and Hodge theory.

(Mar. 26-Apr. 09)

Peter Angelino's notes and homework (optional) on symplectic and hamiltonian actions.

Brian Tran's notes on the Marsden-Weinstein-Meyer theorem.