The Critical 2d Stochastic Heat Flow and other critical SPDEs

Thanks to the theories of Paracontrolled Distributions and Regularity structures we now have a complete theory of  singular SPDEs, which are “sub-critical” in the sense of renormalisation. Recently, there have been efforts to approach the situation of “critical” SPDEs and statistical mechanics models. A first such treatment has been through the study of the two-dimensional stochastic heat equation, which has revealed a certain phase transition and has led to the construction of the novel object called the Critical 2d Stochastic Heat Flow. In this talk we will present some aspects of this model and its construction. We will also present developments relating to other critical SPDEs.

Parts of this talk are based on joint works with Caravenna and Sun and others with Rosati and Gabriel.