# Topological Quantum Field Theory Seminar

### 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

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