The berry connection and other aspects of the Ginzburg-Landau theory in dimension 2

In the first chapter, we analyze the 2-dimensional Ginzburg-Landau vortices at critical coupling, and establish asymptotic formulas for the tangent vectors of the vortex moduli space using theorems of Taubes and Bradlow. We then compute the corresponding Berry curvature and holonomy in the large area limit.In the second chapter, we generalize Bradlow's theorem about existence of irreducible absolute minimizers of the Ginzburg-Landau functional.