Nikos Zygouras University of Warwick
The Euclidean Φ42 theory as the limit of an interacting Bose gas
Abstract:
Thanks to the theories of Regularity Structures, Paracontrolled Distributions
and renormalisation, we now have a complete theory of singular SPDEs, which are “sub-critical”.
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.