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The $L^2$ geometry of vortex moduli spaces

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If you have a question about this talk, please contact Mustapha Amrani .

Moduli Spaces

Let L be a hermitian line bundle over a Riemann surface X. A vortex is a pair consisting of a section of and a connexion on L satisfying a certain pair of coupled differential equations similar to the Hitchin equations. The moduli space of vortices is topologically rather simple. The interesting point is that it has a canonical kaehler structure, geodesics of which are conjectured to approximate the low energy dynamics of vortices. In this talk I will review what is known about this kaehler geometry, focussing mainly on the cases where X is the plane, sphere or hyperbolic plane.

This talk is part of the Isaac Newton Institute Seminar Series series.

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