Yang-Mills-Higgs Equations on General Riemann Surfaces
We study the Yang-Mills-Higgs equations for vector bundles of rank 2 on a Riemann surface of general genus as the punctured Reimann sphere. This work is motivated by the remarkable connection between the Ginzburg-Landau equations for line bundles on elliptic curves and the physical phenomenon of superconductivity. Our generalization also has potential relations to models of the Quantum Hall effects. This is joint work with I.M. Sigal.