Jonathan Herman, Department of Pure Mathematics, University of Waterloo
“Symplectic Reduction”
Symplectic reduction is a process which uses the symmetries of a symplectic manifold to obtain new symplectic manifolds that are in a sense simpler. We will introduce the necessary background material and then give a proof of the Marsden-Weinstein theorem. We will also give a proof of Noether’s theorem in the context of momentum maps, from which we will able to apply the process of reduction to Hamiltonian systems.
MC 5403