Title: 
Ginzburg-Landau vortex dynamics driven by an applied boundary current.

Abstract: This talk concerns recent results on the time-dependent
Ginzburg-Landau equations on a smooth, bounded 2-D domain, subject to
both an applied magnetic field and an applied boundary current. The
boundary current is modeled with a gauge-invariant inhomogeneous Neumann
boundary condition.  The energy of such solutions does not dissipate,
but it is possible to estimate the growth of the energy in time.  This
estimate then allows for the derivation of the dynamics of the vortices
in the limit as the Ginzburg-Landau parameter vanishes.  In an
appropriate time scale, we show that the vortex motion is driven by a
novel Lorentz drift term induced by the presence of the applied boundary
current.