The Vortex Filament Equation in any Dimension

We present the vortex filament (or localized induction approximation) equation in any dimension. For an arbitrary n ≥ 3 the evo- lution of vorticity supported on vortex membranes of codimension 2 in Rn is described by the skew (or binormal) mean-curvature flow, which generalises to any dimension the classical binormal equation in R3. This paper is a brief summary of the results in Khesin (2012) and Shashikanth (2012) [4,6].