Regularity structures and the dynamical $\Phi^4_3$ model

Understand

We give a concise overview of the theory of regularity structures as first exposed in [Hai14].

• In order to allow to focus on the conceptual aspects of the theory, many proofs are omitted and statements are simplified.
• In order to provide both motivation and focus, we concentrate on the study of solutions to the stochastic quantisation equations for the Euclidean $\Phi^4_3$ quantum field theory which can be obtained with the help of this theory.
• In particular, we sketch the proofs of how one can show that this model arises quite naturally as an idealised limiting object for several classes of smooth models.