Geometry Working Seminar

Da Rong Cheng, Department of Pure Mathematics, University of Waterloo

"Non-minimizing solutions to the Ginzburg-Landau equations"

I'll talk about the very recent paper https://arxiv.org/abs/2103.05613v2 by Ákos Nagy and Gonçalo Oliveira, where they use two different methods, one variational and the other perturbative, to construct new examples of non-minimizing critical points of the Ginzburg-Landau functional on Hermitian line bundles over closed Riemannian manifolds. I'll begin with some necessary background on the functional and its Euler-Lagrange equations. Then I'll focus on the second method in the Nagy-Oliveira paper, which uses the Lyapunov-Schmidt reduction and applies in particular to closed manifolds of any dimension with trivial first cohomology.

Zoom meeting: contact Spiro Karigiannis (karigiannis@uwaterloo.ca) or Ragini Singhal (r4singha@uwaterloo.ca) for link