Vortices on Riemann Surfaces

Mr Norman Rink (University of Cambridge)

Friday 4th November, 2011 14:00-15:00 204


It is conjectured that explicit vortex solutions of the abelian Higgs model can be constructed on surfaces of constant negative curvature. In the situation where the surface is non-compact a class of vortex solutions was found by Witten in 1977, and in the compact case integrability of the relevant equations has recently been established. In this talk I will demonstrate how holomorphic maps between surfaces can be used to construct vortex solutions. I will give two fairly explicit examples: one will be on a new non-compact surface, the other one on hyperelliptic curves. Time permitting, I will give an interpretation of our work in view of the Abel-Jacobi map.

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