Singular SPDEs and stochastic calculus: the KPZ equation

Considered one of the most important stochastic processes in the last decades, the KPZ equation has played an enormous role to motivate the study of singular SPDEs, becoming a foundational object in rough analysis. The presence of an explicit solution also made it possible to study its law and most of its properties in detail using standard tools of stochastic analysis. However, the connections between regularity structures and stochastic calculus are still not developed well enough to offer a joint perspective on the KPZ equation, even though both study the same object. In this talk, we will discuss how one can use regularity structures to derive a pathwise change of variable formula for the KPZ equation and some possible interpretations of it. Joint work with Tom Klose (TU Berlin).