Paracontrolled distributions and the KPZ equation

Paracontrolled distributions combine the Fourier techniques of Bony's paradifferential calculus with ideas from the theory of controlled rough paths. This leads to a lightweight calculus for distributions that allows to handle nonlinear operations involving very irregular objects such as white noise, and which allows to give a meaning to and solve singular stochastic partial differential equations. Due to their good continuity properties, paracontrolled distributions are also a powerful tool for studying the convergence of discrete systems to continuum limits. I will present the basic ideas and techniques of paracontrolled distributions and how to apply them to solve the KPZ equation and to prove that it is the limit of the Sasamoto-Spohn discretization. This is joint work with Massimiliano Gubinelli and Peter Imkeller.