Orateur
Description
One possible framework in which to study the Plateau problem is by using currents with multiplicities modulo q, for a fixed integer q. This setting allows for minimizing surfaces to exhibit codimension 1 singularities like triple junctions, which are seen in physical soap films, and has close connections to the known regularity theory for stable minimal submanifolds, while at the same time providing the framework of a minimization problem.
I will give an overview of the history of the problem and discuss recent structural results, including joint work in progress with Luca Spolaor and Salvatore Stuvard for 2-dimensional mod(q) minimizers of arbitrary codimenson, where we are able to obtain a fairly complete local structural picture of the surface and its singular set, in the spirit of the works of Almgren-Chang and De Lellis-Spadaro-Spolaor for two-dimensional area-minimizing integral currents.