Rectifiability of flat singularities for mod(p) area-minimizing hypersurfaces

One possible framework in which to study the Plateau problem is by using currents with mod(p) coefficients, for a fixed integer p. This setting allows for minimizing hypersurfaces to exhibit codimension 1 singularities like triple junctions, and has close connections to the known regularity theory for stable minimal hypersurfaces. Early works on the regularity theory in this framework date back to Federer & L. Simon (p=2), J. Taylor (p=3) and White (p=4), while for general p, the recent work of De Lellis-Hirsch-Marchese-Stuvard-Spolaor leads to a complete structural characterization of the codimension 1 part of the singular set for minimizing hypersurfaces. In this talk, I will discuss the presence of flat singularities in mod(p) area-minimizing hypersurfaces when p is even. Such singularities generally form a codimension 2 set relative to the dimension of the surface. I will discuss some work in progress on establishing a reasonably sharp structural result for such singularities.