TQFTs from Non-Semisimple Modular Categories and Modified Traces - Marco de Renzi

Explore the second lecture in a series on Topological Quantum Field Theories (TQFTs) and modified traces in algebra and topology. Delve into the construction of TQFTs using non-semisimple modular categories and the theory of modified traces. Examine how these advanced mathematical tools provide sophisticated methods for studying topology in dimensions 2 and 3, including the computation of 3-manifold invariants through cut-and-paste techniques and the generation of surface mapping class group representations. Discover how non-semisimple constructions have expanded upon the traditional Reshetikhin-Turaev approach, yielding powerful topological invariants and mapping class group representations with novel properties. Learn about the algebraic foundations of modular categories and their role in TQFT construction, as well as the features of the resulting invariants and representations. This lecture, presented by Marco de Renzi at the Hausdorff Center for Mathematics, is based on collaborative work with A. Gainutdinov, N. Geer, B. Patureau, and I. Runkel.