Lecture series on modified traces in algebra and topology
Topological Quantum Field Theories (TQFTs for short) provide very sophisticated tools for the study of topology in dimension 2 and 3: they contain invariants of 3-manifolds that can be computed by cut-and-paste methods, and their extremely rich structure induces representations of mapping class groups of surfaces. In recent years, so-called non-semisimple constructions have deeply generalized the standard semisimple approach of Reshetikhin and Turaev to the theory, producing powerful topological invariants and representations of mapping class groups with remarkable new properties. In this series of talks, we will explain how to construct a TQFT starting from an algebraic ingredient called (non-semisimple) modular category, and using the theory of modified traces. We will also describe some features of the invariants and representations issued by this construction.
Based on joint works with A. Gainutdinov, N. Geer, B. Patureau, and I. Runkel.
