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19/12/2002, 13:30 — 14:30 — Room P3.10, Mathematics Building

João Baptista, *Cambridge University*

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Vortex dynamics on the sphere

I will first give a brief overview of the Bogomolny equations for vortices, their moduli space of solutions, and the method of geodesic approximation. In the case
of
$N$ vortices on a sphere of radius
${R}^{2}>N$ this moduli space is
$C{P}^{N}$, but the geodesic method cannot be directly applied, because the
solutions of the Bogomolny equations are
not known explicitly. I will then try to show how to circumvent this problem in the limit where
${R}^{2}$ is close to
$N$.

### References

- J. M. Baptista and N. S. Manton,
*The dynamics of vortices on
${S}^{2}$ near the Bradlow limit*, hep-th/0208001.
- T. M. Samols,
*Vortex Scattering*, Commun. Math. Phys. 145, 149 (1992).