Lectures: Wednesdays 9 - 12   BA B025.

Instructor: Professor Yael Karshon
Email:   karshon@math.toronto.edu
Office hours: Mondays 5pm, or by appointment
Office:   BA 6119   (416) 978-7895

Syllabus: We will discuss a variety of concepts, examples, and theorems of symplectic geometry and topology.
These may include, but are not restricted to, these topics:
Review of differential forms and cohomology; Symplectomorphisms; Local normal forms; Hamiltonian mechanics;
Group actions and moment maps; Geometric quantization; A glimpse of holomorphic techniques.

Non-inclusive list of relevant books:

• Ana Cannas da Silva, Lectures on Symplectic Geometry, Lecture Notes in Mathematics 1764, Springer-Verlag 2001.
• Dusa McDuff and Dietmar Salamon, Introduction to Symplectic Topology, Oxford Science Publications.
• 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.

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

Crash course on manifolds:   postscript,   pdf.
Crash course on flows:   postscript,   pdf.

Student presentation summaries.
Kristin Shaw: Polarizations
Siddarth Sankaran: Hofer metric
Michael Bailey: Capacities
Jordan Watts: Poisson geometry
Travis Li: Deformation quantization
Yuri Burda: Gompf construction
Kathleen Smith: Morse theory and equivariant cohomology.   overheads .
Pablo Carrasco: Geodesic flow
Leonid Shartser: Ellipsoids

Two-page course summary .

Lecture notes, by Travis Li. (Any mistakes that might occur in the notes are Yael's fault.) Week 1 ,   Week 2 ,   Week 3 ,   Week 4 ,   Week 5 ,   Week 6 ,   Week 7 ,   Week 8 ,   Week 9 ,   Week 10,   Week 11,   Week 12,   Week 13.