Graduate School in Nonlinear Science

Sponsored by The Danish Research Agency

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

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.