TQFTs from Non-Semisimple Modular Categories and Modified Traces - Lecture I

Explore the first 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. Learn how these advanced mathematical tools provide sophisticated methods for studying topology in dimensions 2 and 3, including invariants of 3-manifolds and representations of mapping class groups of surfaces. Discover recent developments in non-semisimple constructions that have significantly expanded the standard semisimple approach of Reshetikhin and Turaev, leading to powerful new topological invariants and representations with remarkable properties. Gain insights into the algebraic foundations of TQFTs and their applications in topology, based on joint works with A. Gainutdinov, N. Geer, B. Patureau, and I. Runkel.