Dynamics near criticality

The theory of regularity structure and the notion of paracontrolled distribution introduced respectively (and independently) by M.Hairer and M.Gubinelli, P.Imkeller, N.Perkowski allow to study the well-posedness of a large class of singular parabolic stochastic partial differential equations. The aim of the talk is to discuss the context for which theses new technique can be used and what kind of existence result is obtained by using this two approach and namely we will focus on the spectral theory of Schrödinger operator with white noise potential.