Modular categories and TQFTs beyond semisimplicity

  • Christian Blanchet

    Sorbonne Université, Paris, France
  • Marco De Renzi

    Universität Zürich, Switzerland
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Vladimir Turaev discovered in the early years of quantum topology that the notion of modular category was an appropriate structure for building 3-dimensional Topological Quantum Field Theories (TQFTs for short) containing invariants of links in 3-manifolds such as Witten– Reshetikhin–Turaev ones. In recent years, generalized notions of modular categories, which relax the semisimplicity requirement, have been successfully used to extend Turaev’s construction to various non-semisimple settings. We report on these recent developments in the domain, showing the richness of Vladimir’s lineage.