Triangle Seminars

Abstract:
The equations for Abelian Higgs vortices (magnetic flux vortices) on a plane
or a more general surface are generally not integrable, but for vortices
on a hyperbolic plane of curvature -1/2 they are. This talk will
present (almost explicit) vortex solutions on certain compact hyperbolic
surfaces. Also to be discussed are two asymptotically solvable problems
for vortices: the effective vortex motion on a large surface with
small curvature, and the structure of vortex solutions on a small
surface where the vortices are about to dissolve (and the equations
linearize).

These results (obtained with N. Rink and with N. Romao) bring vortex
theory closer to classical results on the complex and metric geometry
of Riemann surfaces.

Abstract:
We reformulate M-theory in a duality manifest way using generalised
geometry.