# The $L^2$ geometry of vortex moduli spaces

Presented by:
M Speight [Leeds]
Date:
Thursday 24th February 2011 -
15:30 to 16:30
Venue:
INI Seminar Room 1
Abstract:
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.
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