Description
The static Phi^4 model on the d-dimensional torus is a well-known toy
model in Euclidean quantum field theory. It is well-posed for d = 1,
and its renormalisation is well-understood for d = 2 and d = 3, thanks
to works by Glimm, Jaffe, and many others. In the dynamic case, the
model becomes a stochastic PDE, motivated by the idea of stochastic
quantization. It is well-posed for d = 1. A proof of existence of
solutions to a renormalised version for d = 2 has been obtained by
Da Prato and Debussche in 2003, while the case d = 3 was first solved
by Martin Hairer in 2014, using his theory of regularity structures.
I will provide an overview of these results, focusing on algebraic
techniques of the proofs, and briefly address more general recent
results on renormalisation of singular SPDEs.
The talk is partly based on the book
https://ems.press/books/elm/232
