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The (1+2)-dimensional abelian Yang-Mills-Higgs model is a classical relativistic field theory that features topological soliton solutions called vortices. We discuss a proof of the asymptotic stability for the degree-one vortex under equivariant perturbations in the so-called self-dual case.

This is joint work in preparation with J. Palacios, F. Pusateri, W. Schlag, and S. Shahshahani