MIDIT OFD CATS Modelling, Nonlinear Dynamics Optics and Fluid Dynamics Chaos and Turbulence Studies and Irreversible Thermodynamics Risø National Laboratory Niels Bohr Institute and Technical University of Denmark Building 128 Department of Chemistry Building 321 P.O. Box 49 University of Copenhagen DK-2800 Lyngby DK-4000 Roskilde DK-2100 Copenhagen Ø Denmark Denmark Denmark
by Annalisa Calini
Department of Mathematics,
College of Charleston,
Charleston, SC 29424
Tuesday, July 3, 2001, 15.00 h
at IMM, Bldg. 305, Room 018, DTU
Abstract: The dynamics of vortex filaments has provided for almost a century one of the most interesting connections between differential geometry and integrable equations, and an example in which knotted curves arise as solutions of differential equations possessing remarkably rich geometrical structures. This talk has two threads. First, a discussion of soliton equations in a concrete geometrical setting. Second, an illustration of how techniques of integrable systems can be used to investigate geometrical and topological properties of closed curves and to obtain canonical representatives for many classes of knots.