Fermionic Modular Categories and the 16-fold Way
  We study spin and super-modular categories systematically as inspired by fermionic topological phases of matter, which are always fermion parity enriched and modelled by spin TQFTs at low energy. We formulate a $16$-fold way conjecture for the minimal modular extensions of super-modular categories to spin modular categories, which is a categorical formulation of gauging the fermion parity. We investigate general properties of super-modular categories such as fermions in twisted Drinfeld doubles, Verlinde formulas for naive quotients, and explicit extensions of $PSU(2)_{4m+2}$ with an eye towards a classification of the low-rank cases. 
Paul Bruillard, Cesar Galindo, Tobias Hagge, Siu-Hung Ng, Julia Yael   Plavnik, Eric C. Rowell, Zhenghan Wang
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