Compactification of the moduli spaces of vortices and coupled vortices
  Vortices and coupled vortices arise from Yang-Mills-Higgs theories and can be viewed as generalizations or analogues to Yang-Mills connections and, in particular, Hermitian-Yang-Mills connections. We proved an analytic compactification of the moduli spaces of vortices and coupled vortices on hermitian vector bundles over compact K\"ahler manifolds. In doing so we introduced the concept of ideal coupled vortices and characterized the singularities of ideal coupled vortices as well as Hermitian-Yang-Mills connections. 
Gang Tian and Baozhong Yang