Partial regularity of area-minimizing currents mod p

I will discuss a first general partial regularity theorem for area minimizing currents mod p, for every p, in any dimension and codimension. Our main result establishes that the interior singular set of m-dimensional area minimizing currents mod p has at most Hausdorff dimension m-1. Moreover the interior singular set is rectifiable and of locally finite Hausdorff measure for odd values of p. Joint work with Camillo De Lellis, Jonas Hirsch, and Salvatore Stuvard.