Thomas KRAJEWSKI - Connes-Kreimer Hopf Algebras...

Connes-Kreimer Hopf Algebras : from Renormalisation to Tensor Models and Topological Recursion

At the turn of the millenium, Connes and Kreimer introduced Hopf algebras of trees and graphs in the context of renormalisation. We will show how the latter can be used to formulate the analogue of Virasoro constraints for random tensors, which are natural generalisations of random matrices. Motivated by this example, we will also sketch how these algebras appear in the formulation of topological recursion proposed by Kontsevich and Soibelman.