Algebraic renormalisation of regularity structures

The regularity structures introduced by Martin Hairer allow us to describe the solution of a singular SPDEs by a Taylor expansion with new monomials. We present the two Hopf Algebras used in this theory for defining the structure group and the renormalisation group. We will point out the importance of recursive formulae with twisted antipodes. This is a joint work with Martin Hairer and Lorenzo Zambotti.