Probability and Mathematical Physics Seminar

The Critical 2d Stochastic Heat Flow and other critical SPDEs

Speaker: Nikos Zygouras, University of Warwick

Location: Warren Weaver Hall 1302

Date: Friday, March 29, 2024, 11:10 a.m.


Thanks to the theories of  Regularity Structures, Paracontrolled Distributions 
and Renormalisation we now have a robust framework for 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 a variety of structures that underlie the critical dimension and
some further 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.