Written by leading experts in an emerging field this book offers a unique view of the theory
of stochastic partial differential equations with lectures on the stationary KPZ equation
fully nonlinear SPDEs and random data wave equations. This subject has recently attracted a
great deal of attention partly as a consequence of Martin Hairer's contributions and in
particular his creation of a theory of regularity structures for SPDEs for which he was
awarded the Fields Medal in 2014. The text comprises three lectures covering: the theory of
stochastic Hamilton-Jacobi equations one of the most intriguing and rich new chapters of this
subject singular SPDEs which are at the cutting edge of innovation in the field following the
breakthroughs of regularity structures and related theories with the KPZ equation as a central
example and the study of dispersive equations with random initial conditions which gives new
insights into classical problems and at the same time provides a surprising parallel to the
theory of singular SPDEs viewed from many different perspectives. These notes are aimed at
graduate students and researchers who want to familiarize themselves with this new field which
lies at the interface between analysis and probability.
