The vortex filament equation (VFE) is a geometric equation that describes the evolution of a curve of vorticity in a three dimensional incompressible inviscid fluid. Through the Hasimoto transformation, the VFE is associated with the cubic NLS equation. In this talk I will focus my attention on vortex filaments that are initially polygonal lines, which correspond to studying the cubic NLS with sum of delta of Dirac as initial data. In particular I will show local and large in time well-posedness for sufficiently small initial data in appropriated spaces. This is a joint work with Luis Vega.
