Towards a gauge-theoretic approximation of codimension-three area

In the last three decades, a fruitful way to approximate the area functional in low codimension is to interpret submanifolds as the nodal sets of maps (or sections of vector bundles), critical for suitable physical energies or well-known lagrangians from gauge theory. Inspired by the situation in codimension two, where the abelian Higgs model has provided a successful framework, we look at the non-abelian SU(2) model as a natural candidate in codimension three. In this talk we will survey the new key difficulties and some recent partial results, including a joint work with D. Parise and D. Stern and another result by Y. Li.