Matt Young, Utah State

Title: Z-hat invariants for Lie superalgebras

Abstract: The goal of this talk is to explain a representation theoretic approach to physicists' so-called Z-hat invariants of 3-manifolds, as introduced by Gukov, Pei, Putrov and Vafa in the context of supersymmetric gauge theory. Specifically, we use the representation theory quantum supergroups to construct non-semisimple analogues of the modular tensor categories Reshetikhin, Turaev, Andersen and others. These categories can in turn be used to construct quantum invariants of 3-manifolds, certain limits of which recover the Z-hat invariants. Based on joint work with Francesco Costantino, Matthew Harper and Adam Robertson.