University of Toronto

Introduction to Symplectic Geometry, Winter 2021


Student presentations

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

Instructor: Yael Karshon
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.