Bessel SPDEs and renormalized local times

Bessel processes are a classical family of stochastic diffusions obeying singular dynamics which, in a certain regime, involve a remarkable renormalization procedure. More recently a family of stochastic PDEs related to Bessel processes has been introduced, the dynamics of which involve similar but more acute renormalizations. In my talk I shall introduce these processes and explain the remarkable underlying structure. Applications to scaling limits of dynamical critical wetting models will be mentionned. This is based on joint work with Lorenzo Zambotti.