School of Mathematical Sciences

Department Colloquium

Melamed Hall, 12:30

University of Toronto

Symplectic 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.

Abstract:

In control 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.

In algebraic geometry, toric varieties that are associated to rational convex polytopes can be obtained as symplectic reductions of ℂ^{n}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.