Symplectic Geometry

Instructor: Joel Kamnitzer, jkamnitz@math.toronto.edu
Lectures: Tu 3-4:30pm AP 120, Th 2-3:30 pm WI 524
Office: 6246 Bahen 416-978-3998
Office Hours: Mondays 3 - 4 pm, Wednesdays 3 - 4 pm

Grading scheme:

  • Homework (every 2-3 weeks) 60%
  • Take home final 40%

    • Text: Ana Cannas da Silva, Lectures on Symplectic Geometry

    Other useful references:
  • Michele Audin, "Topology of torus actions on symplectic manifolds"
  • Raymond Wells, "Differential Analysis on Complex Manifolds"
  • Eckhard Meinrenken, Symplectic geometry
  • Allen Knutson, The symplectic and algebraic geometry of Horn's problem

    • Syllabus: (with sections from the text)
    Basic definitions, examples, Hamiltonian vector fields, local theory (1-3, 6-9, 18)
    Complex geometry, compatible triples, Kahler geometry, Hodge theory (12-17)
    Group actions, moment maps, symplectic reduction, toric varieties (21-30)

    Homework:
    Homework 1, due Jan 22.
    Homework 2, due Feb 12.
    Homework 3, due Mar 12.
    Howework 4, due Mar 31.
    Take-home final, due Apr 9.