# 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.

**Synopsis:**

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

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.

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