Adam Morgan, Department of Applied Mathematics, University of Waterloo
"Classical Field Theory from the Hamiltonian Viewpoint"
In this talk, we introduce basic elements of the theory of infinite-dimensional Hamiltonian dynamical systems, with an eye towards applications in fluid mechanics. First, we will briefly review the Hamiltonian formulation of classical mechanics. From there, we give an abstract definition of the variational derivative encountered in elementary physics. Next, we move on to define Poisson algebras, which serve as the classical field theory analogue of phase spaces. We then show how the shallow water equations from geophysics may be understood as a Hamiltonian system. Finally, we conclude by providing an overview of the connection between diffeomorphism groups and Hamiltonian descriptions of ideal fluids.
MC 6460