School of Mathematical Sciences
Monday, May 23, 2016
Melamed Hall, 12:30
University of Toronto
Symplectic reduction - old and new
manifolds provide the mathematical models for phase space in classical
mechanics. Symplectic reduction with respect to a symmetry group is a
procedure for passing to a sub-quotient. This procedure has
surprisingly broad relevance.
theory, a falling cat lands on its feet by suitably moving its body
within the space of its possible shapes; the explanation involves
symplectic reduction of the cat's phase space.
algebraic geometry, toric varieties that are associated to rational
convex polytopes can be obtained as symplectic reductions of ℂn with respect to rotations of the coordinates at appropriate speeds.
I will give you a glimpse of the symplectic reduction procedure,
concluding with an open question on the intrinsic geometry of the
resulting reduced spaces.
Coffee will be served at 12:00 before the lecture
near Melamed Hall.
Even before, between 11:00-12:00, Shira Tanny will give an introductory talk, intended mainly for students without a firm background in symplectic geometry.