# GEOMETRY & TOPOLOGY AT PRINCETON: Min-Max constructions for Ginzburg-Landau functionals and applications to geometric measure theory

The Ginzburg-Landau functionals (with no magnetic field) are a one-parameter family of functionals defined on complex-valued maps, whose variational theory is connected to that of the Dirichlet energy for S^1-valued maps and the area functional for submanifolds of codimension two. We describe a natural min-max method for producing critical points of these functionals on a given manifold, and discuss applications to the existence of critical points of the codimension-two area functional.