Fermionic phases of matter and bosonization Anton Kapustin California Institute of Technology Physics I outline the classification of Short-Range-Entangled topological phases of interacting fermions in 1-,2-,and 3-spatial dimensions. From the mathematical point of view, this problem boils down to computing spin-cobordism groups of the classifying space of the symmetry group. I describe a physical approach to this problem and explain the relevance of higher-form symmetries.