Séminaire Physique mathématique ICJ

Topological Quantum Field Theories and Higher Categories

par Alessandro Valentino (Universität Zürich)

Fokko du Cloux (Institut Camille Jordan)

Fokko du Cloux

Institut Camille Jordan

Université Lyon 1, Bât. Braconnier, 21 av. Claude Bernard, 69100 Villeurbanne
TQFTs have been axiomatized by Atiyah and Segal as functors from a category of cobordisms to a category of algebraic objects, e.g. vector spaces, in order to describe the formal properties of the path integral for quantum field theories which do not depend on any metric structure. In the talk I will discuss extended TQFTs, which are a generalization of the notion of TQFT which have "more" locality, and the higher categorical objects necessary to formulate them. I will also comment on the relation between extended TQFTs, modular tensor categories and invertible quantum field theories, with an eye towards applications to condensed matter physics.