The integer quantum Hall states, the quantum spin Hall insulator, and the (2+1)D p-wave topological superconductor each have an important place in condensed matter physics due to their quantized symmetry-protected topological invariants. These systems have a unique ground state on any closed manifold in (2+1) dimensions, and are examples of 'invertible' topological phases of fermions. Here I will describe a general theory which fully encodes the universal properties of such invertible phases, and classifies them based on their symmetries. This approach is 'categorical': it does not require solvable microscopic models, and is applicable to systems with arbitrarily strong interactions. Some new applications of the theory include an interacting version of the 'tenfold way' classification of topological insulators and superconductors, and also the prediction of an interesting invertible phase which by our naïve intuition should not exist (but apparently does).
Reference: https://arxiv.org/abs/2109.11039
Pizza and drinks served after the talk.