Vortices on Riemann Surfaces

Mr Norman Rink (University of Cambridge)

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

Abstract

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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