Geometry and gauge theory of skyrmions

The Skyrme model is a model of nuclei based on an energy functional whose critical points, skyrmions, may be understood as a generalisation of harmonic maps. In this talk I shall introduce the model and discuss how tools from differential geometry and gauge theory (such as the ADHM construction of instantons) are used to study its properties, and can address long-standing problems with the theory. If time permits, I shall discuss some new results regarding how to correctly couple a gauge field to the model; an important consideration for studying realistic physical phenomena such as electromagnetic and electroweak properties of nuclei.