Students' final presentations:
  Peter Crooks: Stratified symplectic spaces and reduction.
  Arthur Huang: The Hofer Zehnder theorem on existence of periodic orbits.
  Alexander Caviedes: Symplectic Lefschetz fibrations.
  Robin Chhabra: Non-holonomic mechanics.

Lectures: (The locations are not my fault!)
    Wednesdays 1-3 pm, HA 401 (see this map) except Feb.16.
        (Wed Feb.16: AP120, just northwest of the Bahen Centre.)
    Fridays 1-2, BA3008.

Instructor: Professor Yael Karshon
Email:   karshon@math.toronto.edu
Office hours: after class or by appointment.
Office:   BA 6119   (416) 978-7895

Syllabus: In the first part of the course, we will give Gromov's non-squeezing theorem,
assuming a few "black boxes" from analysis. On our way we will cover
basic definitions and examples, Moser's method and Darboux's theorem,
almost complex structures, Wirtinger's inequality and its consequences,
and Gromov compactness.
We will then turn to more classical topics, such as Hamiltonian mechanics,
group actions and momentum maps, or geometric quantization.

Non-inclusive list of relevant books and sources:

• Ana Cannas da Silva, Lectures on Symplectic Geometry, Lecture Notes in Mathematics 1764, Springer-Verlag 2001.
• Eckhard Meinrenken, Lecture notes in Symplectic Geometry.
• Dusa McDuff and Dietmar Salamon, Introduction to Symplectic Topology, Oxford Science Publications.
• Dusa McDuff and Dietmar Salamon, J-holomorphic curves and symplectic topology
• B.Aebischer, M.Borer, M.Kälin, Ch.Leuenberger, H.M.Reimann, Symplectic geometry, an introduction based
  on the seminar in Bern in 1992; Birkhäuser 1994.
• V.I.Arnold, Mathematical Methods of Classical Mechanics, Second Edition.
• Helmut Hofer and Eduard Zehnder, Symplectic Invariants and Hamiltonian Dynamics, Birkhäuser, 1994.
• Viktor Ginzburg, Victor Guillemin, and Yael Karshon, Moment maps, cobordisms, and Hamiltonian group actions,
  American Mathematical Society Mathematical Surveys and Monographs 98.
• Hamiltonian Group Actions, winter 2009-10, (rough!) notes.

Requirements for credit: participation, assignments, presentations and written summaries.

Crash course on manifolds:   pdf.
Crash course on flows:   pdf.
Review of homology:   pdf.