Walter Craig (McMaster University) will present "Vortex filament interactions and Hamiltonian PDEs." Abstract: In this talk I will describe a problem in mathematical fluid dynamics, having to do with a model of the interactions of two near-parallel vortex filaments. The equations of motion can be formulated as a Hamiltonian PDE, giving rise to a Hamiltonian system with infinitely many degrees of freedom. Over the past decade and more, techniques have been developed for the phase space analysis of the flow of similar equations. I will describe a KAM theory for solutions to the vortex equations in this setting, and use the occasion to speculate about further applications of Hamiltonian PDEs to other nonlinear systems and evolution problems in fluid dynamics.