Fun with fractons

Interest in fracton topological order has grown explosively over the past several years, leading to a plethora of models that exhibit exotic topological physics tied to mobility constrained superselection sectors. At the same time a classification of even the simplest class of stabilizer fracton Hamiltonians remains elusive. I will describe some recent efforts to tame the vast array of models with the goal of a systematic construction and classification of all topological phases of matter in three spatial dimensions.