Dynamics of Ginzburg Landau vortices for vector fields on surfaces.
In this talk I will report on a joint work with Giacomo Canevari (Univ. Verona). I will discuss a parabolic Ginzburg-Landau equation for vector fields on a 2 dimensional closed and oriented Riemannian manifold. In a suitable asymptotic regime the energy of the solutions concentrates on a finite number of points. These points are called vortices and I will show that their evolution is governed by gradient flow of the so-called renormalized energy.