Derived topological theories in dimension 3

Abstract: I will discuss ongoing work on constructions of (Reshetikhin-Turaev style) TQFTs from derived categories of quantum group representations. Such theories can be constructed, at least in part, by “deriving” non-semisimple TQFTs from De Renzi et al. This derivation process is more or less complicated depending on whether one operates at the 1-categorical, or $\infty$-categorical level. I will try to focus on a view towards the future, where we might anticipate theories in both dimensions 3 and 4 for any “modular $\infty$-category”, and an accompanying skein theory for such categories.

Mathematics

Audience: researchers in the topic

European Quantum Algebra Lectures (EQuAL)

Series comments: EQuAL is an online seminar series on quantum algebra and related topics such as topological and conformal field theory, operator algebra, representation theory, quantum topology, etc. sites.google.com/view/equalseminar/home