Séminaires Mathématique 2010-2011

  Mercredi 16 Février à 14h30, salle 114

Winston Fairbairn (Dept. of Math., University of Hamburg) : Quantum deformation of spin foam models

Invariants of topological manifolds that are based on the representation theory of quantum groups play an important role in mathematical physics. In particular, they are of interest to quantum gravity, where they are known under the name of spin foam models. Compared to the `classical’ models which are based on the representation theory of Lie groups, the q-deformed models constructed upon the representation categories of quantum groups offer several advantages, the most important one being the improvement of the convergence properties. In this talk, I will discuss q-deformations of spin foam models in three and four space-time dimensions. I will firstly review the derivation of the Ponzano-Regge model of 3d quantum gravity from a physical perspective and present the Turaev-Viro invariant as a natural regulator of its divergences. I will then discuss analogue constructions in four dimensions and present recent results concerning the q-deformation of a certain constrained topological model.