### Vortices on Riemann Surfaces

Manton, N *(Cambridge)*

Wednesday 29 June 2011, 10:00-11:00

Seminar Room 1, Newton Institute

#### Abstract

We will discuss the geometry and physics of U(1) vortex solutions on compact Riemann surfaces. The moduli space of N-vortex solutions has a natural Riemannian metric, for which there is a localised expression (Samols-Strachan) although this is not known explicitly. The volume of the moduli space is known, leading to an equation of state for a vortex gas. An asymptotic expression for the moduli space metric for one vortex on a large surface has been obtained, which could be developed further (Dunajski & Manton). The metric is also understood in the limit of a small surface, where the vortex dissolves (Manton & Romao).

#### Presentation

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