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

Lectures: Wednesdays 9 - 12   Sidney Smith Hall (100 St.George Street) Room 1074.

Instructor: Professor Yael Karshon
Email:   karshon@math.toronto.edu
Office hours:   Wednesdays 12-1 or by appointment
Office:   Sidney Smith Room 4070   (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, final project.

Student projects:

• Symplectic linear algebra, Dan Carney.
• Symplectic fibrations, Xiaolong Cheng.
• The Gelfand-Dikey bracket, Dmitry Donin.
• Generalized complex structures, Sean Fitzpatrick.
• Lie algebra cohomology, Shay Fuchs.
• The Arnold conjecture, Garry Goldstein.
• Electromagnetism and symplectic geometry, Andy Hammerlindl.
• The figure eight solution of the three-body problem, Paul Lee.
• Symplectic toric manifolds, Chao Li.
• Hodge theory for Kahler manifolds, Pinaki Mondal.

                Symplectic Geometry: lunches, seminar talks, conferences