### University of Toronto

## Introduction to Symplectic Geometry, Winter 2021

(MAT1344HS)

**Student presentations**

**Lectures:** Wednesday 12-2 and Friday 1-2
``Make-up day'': Monday April 12, 1-2 pm.

**Instructor:** Yael Karshon

**Email:** karshon@math.toronto.edu

**Office hours:** Friday after class, or by appointment

**Zoom link:** see Quercus, or ask me

**Syllabus:** This is an introductory course in symplectic
geometry and topology. We will discuss a variety of concepts,
examples, and theorems, which may include, but are not restricted to,
these topics:
Moser's method and Darboux's theorem;
Hamiltonian group actions and momentum maps;
almost complex structures and holomorphic curves;
Gromov's nonsqueezing theorem.

**Prerequisites:** Manifolds and differential forms; homology.

**Requirements for credit:**
Participation, assignments, presentations and written summaries.

Suggestions for projects

** Non-inclusive list of relevant books:**
John Lee, "Introduction to Smooth Manifolds", 2nd edition, 2013,
Chapter 22 ("Symplectic Manifolds").
Alan Weinstein, Lectures on Symplectic Manifolds, 1977.
Anna Cannas da Silva,
Lectures on Symplectic Geometry, corrected 2nd printing, 2008.
Eckhard Meinrenken, lecture notes on Symplectic Geometry, on his website.
Victor Guillemin and Shlomo Sternberg,
"Symplectic Techniques in Physics", 1984.
Dusa McDuff and Dietmar Salamon, "Introduction to Symplectic Topology",
3rd Edition, 2017.
Helmut Hofer and Eduard Zehnder,
"Symplectic invariants and Hamiltonian dynamics", 1994.
B. Aebischer, M. Borer, M. Kalin, C. Leuenberger, and H.M.Bach,
"Symplectic Geometry, an introduction based on the seminar in Bern, 1992".

**Lecture notes:**
13Jan2021,
15Jan2021,
20Jan2021,
22Jan2021,
27Jan2021,
29Jan2021,
03Feb2021,
05Feb2021,
10Feb2021,
12Feb2021,
24Feb2021
(a-synchronous),
26Feb2021,
03Mar2021,
05Mar2021,
10Mar2021,
12Mar2021,
17Mar2021,
19Mar2021,
24Mar2021,
26Mar2021,
31Mar2021,
07Apr2021,
09Apr2021,
12Apr2021

Here is a three-page LaTeX sample file and the resulting pdf:
latex-samplefile.tex,
latex-samplefile.pdf.