$\widehat{Z}$-invariants for Lie superalgebras

Abstract: The goal of this talk is to explain a representation theoretic approach to physicists' so-called $\widehat{Z}$-invariants of $3$-manifolds, as introduced by Gukov, Pei, Putrov and Vafa in the context of $3$d $\mathcal{N}=2$ 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 $\widehat{Z}$-invariants. I will focus on specific examples and will not assume any familiarity with quantum topology. Based on joint work with Francesco Costantino, Matthew Harper and Adam Robertson.

number theoryrepresentation theory

Audience: researchers in the topic

University of Utah Representation Theory / Number Theory Seminar