In this talk, we will discuss the asymptotic behavior of the SU(2)-Yang-Mills-Higgs energies in the large mass limit, and see how they converge to the codimension three area functional in the sense of De Giorgi’s Gamma-convergence. This is motivated by analogous phenomena in the codimension one (i.e. Allen-Cahn) and codimension two (i.e. Ginzburg-Landau and abelian Yang-Mills-Higgs) settings. To illustrate the geometric content of this convergence result, we will see that area-minimizing (n − 3)-cycles can be approximated locally by minimizers (or minimizing sequences) for the SU(2)-Yang–Mills–Higgs energy; in other words, Plateau’s problem in codimension three can be solved by gauge-theoretic means. These results provide evidence for predictions of Donaldson and Segal in the setting of G2 manifolds and Calabi-Yau 3-folds. The talk is based on joint work with A. Pigati, and D. Stern.