ON KNOTTED VORTEX FILAMENTS AND THEIR STABILITY PROPERTIES - ANNALISA CALINI - COLLEGE OF CHARLESTON - US

The Vortex Filament Equation (VFE), modeling the self-induced dynamics of a vortex filament in an ideal
fluid, is a simple but important example of integrable geometric flow for space curves. Its connection with the
focusing cubic Nonlinear Schrödinger Equation through the well-known Hasimoto transformation allows the use of tools
from soliton theory to construct and investigate finite-gap and soliton solutions. This talk will discuss
the construction and the linear stability properties of a family a knotted vortex filaments, including torus and
cable knots, whose knot type does not change under the VFE evolution. This is joint work with Tom Ivey and Stephane
Lafortune.