PIMS - USaskatchewan Applied Math Seminar: Ákos Nagy

Ginzburg–Landau theory is one of the oldest models in classical field theory for spontaneous symmetry breaking through the Higgs mechanism. Minimizers of the Ginzburg–Landau free energy, called vortices, are well-understood, especially in 2 dimensions. Much less is known about nonminimal solutions. On the flat plane no such solution exists, but this is not true on compact domains. Motivated by (and building on) works of Sigal et al. and Taubes, I give conditions for the non/existence of nonminimal solutions. Moreover, I compute approximate forms of such solutions. Part of this work is joint with Gonçalo Oliveira.