Boris Khesin, University of Toronto
The binormal (or vortex filament) equation provides the localized induction approximation of the 3D incompressible Euler equation. We present a Hamiltonian framework for the binormal equation in higher-dimensions and its explicit solutions that collapse in finite time. On the other hand, by going to lower dimensions, we observe a curious appearance of the golden ratio in the motion of point vortices in the plane. We also describe a puzzle relating Hamiltonian approximations and seeming attractors in 2D ideal hydrodynamics.