Renormalization "Ã la Dyson" and Hopf algebras

This talk has two aims: on one side to sketch the long way from elementary particles to combinatorial Hopf algebras, through an overview accessible to non-specialists. On the other side, to present a very personal mathematical interpretation of the renormalization formulas proved by Freeman Dyson in '49 for quantum electrodynamics, which fully justify the appearance of Faà di Bruno and Connes-Kreimer Hopf algebras in this context.