Geometry and Topology Seminar

The complex Ginzburg-Landau equations are a family of geometric pdes arising in the study of harmonic maps, as well as simple models of superconductivity and superfluids. Around 20 years ago, it was observed that families of solutions satisfying natural energy bounds exhibit energy concentration along certain generalized minimal submanifolds of codimension two. Since then, it has been an open question whether energy is quantized along these concentration sets, in the sense that the limiting energy measure has integer multiplicity almost everywhere. In this talk, I'll describe joint work with Alessandro Pigati showing that this quantization does not hold in general, but that quantization does hold where energy density is <2.