Symplectic Geometry and Topology

Linear symplectic geometry and linear Hamiltonian systems. Symplectic manifolds and their Lagrangian submanifolds, local properties. Symplectic geometry and mechanics. Contact geometry and contact manifolds. Relations between symplectic and contact manifolds. Hamiltonian systems with symmetries. Momentum map and its properties. May be repeated for credit. NOTE: Undergraduates and Masters students who wish to enroll must fill out a Request for Review form: https://forms.gle/v5RojToYzmYxGvKc7 ; Your request will be reviewed by faculty and you'll be notified if you are granted permission to enroll.