Colloquium at Tor Vergata: Walter Craig (McMaster University) 12 Sept 2016

DEPARTMENT COLLOQUIUM

12 SEPTEMBER 2016 , 15.00 (A refreshment will follow in the common room)

AULA DAL PASSO - DEPARTMENT OF MATHEMATICS

UNIVERSITA’ DI ROMA “TOR VERGATA”

Speaker: Prof. Walter Craig (McMaster University)

Title: Vortex Filament Dynamics

Abstract The evolution of vortex filaments in three dimensions is an important problem in mathematical hydrodynamics. It appears in questions on solutions of the Euler equations as well as in the fine structure of vortex filamentation in a superfluid. It is also a setting in the analysis of partial differential equations with a compelling analogy to Hamiltonian dynamical systems. I will give an analysis of a system of model equations for the dynamics of near-parallel vortex filaments in the Euler flow of a three dimensional fluid.  These equations can be formulated as a Hamiltonian system of partial differential equations. My talk will describe some aspects of a phase space analysis of solutions, including the construction of periodic and quasi-periodic orbits via a version of KAM theory for PDEs, and a topological principle to count multiplicity of solutions. This is ongoing joint work with L. Corsi (Georgia Tech), C. Garcia (UNAM), C.-R. Yang (McMaster and Shantou University).