Abstract: 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.

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 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.