Some algebra behind non-semisimple TQFTs

par M. Nathan Geer

mardi 25 juin 2024, 11:15 → 12:15 Europe/Paris

Salle Pellos (Salle Pellos)

In this talk I will give an introductory lecture on constructing Topological Quantum Field Theories (TQFTs) from non-semisimple categories. The main goal of the talk is to give a hint of what is needed to extend the Turaev-Viro and Crane-Yetter TQFTs from the useful setting of semisimple categories to the non-semisimple world. I will do this from an algebraic and categorical point of view. In particular, I will discuss what kind of structures are needed in non-semisimple categories to give rise to (2+1)-TQFTs. Then I will remark that any spherical tensor category (in the sense of Etingof, Douglas et al.) has such structures. This work is joint with Francesco Costantino, Benjamin Haïoun, Bertrand Patureau-Mirand and Alexis Virelizier and based on arXiv:2302.04509 and arXiv:2306.03225.