An entire solution to the Ginzburg-Landau system in three dimensions with a singular nodal set

We show how to construct an entire saddle solution to the complex Ginzburg-Landau system in three dimensions, whose zero set is the union of two perpendicular, intersecting lines, and whose blow-downs concentrate on these lines with multiplicity one. This is achieved as the limit of a sequence of minimum problems in a space of functions with suitable symmetries. The talk is based on a joint work with Michele Caselli (SNS).