The University of Arizona
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Yang-Mills-Higgs Equations on General Riemann Surfaces

Mathematical Physics and Probability Seminar

Yang-Mills-Higgs Equations on General Riemann Surfaces
Series: Mathematical Physics and Probability Seminar
Location: MATH 402
Presenter: Nick Ercolani, University of Arizona

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.