Quantum Mathematics Seminar: Azat Gainutdinov (Tours)

Quantum Maths Seminar, external speaker.

Speaker: Azat Gainutdinov (Universite de Tours, CNRS) 

Title: 3-Dimensional Topological QFTs from Non-Semisimple Modular Categories

Abstract: The famous Reshetikhin-Turaev (RT) construction produces a 3d Topological QFT out of a semi-simple modular tensor category. In the middle of 90's Lyubashenko has proposed a reasonable non-semisimple version of modular tensor categories and showed that they produce representations of mapping class groups of oriented surfaces. Many important examples of such categories come as representation categories of small quantum groups at roots of unity (no truncation is needed). However, a proper TQFT construction for Lyubashenko's theory was missing. In a joint work with M. De Renzi, N. Geer, B. Patureau-Mirand, and I. Runkel, we proposed such non-semisimple 3d TQFTs defined on so-called admissible cobordisms and showed that they reproduce the mapping class group representations of Lyubashenko. In the talk, I will also discuss interesting features of these representations not present in the RT construction, e.g. infinite order of Dehn twists action, and associated topological invariants of a few 3-manifolds, e.g. the lens spaces (a recent joint work with J. Berger and I. Runkel).

One-hour in-person talk