Global well-posedness of the dynamic $\Phi^4$ model in the plane

In the first half of this talk a new approach to construct solutions to the two dimensional stochastic quantisation equation in the whole plane will be discussed. The quantisation equation is a non-linear stochastic PDE that can only be interpreted in a ``renormalised'' sense. Following an idea by Da Prato and Debussche we reduce the problem to solving a PDE with random coefficients. We then show existence and uniqueness for this equation in a suitable Besov space with weights. In the second half I will discuss how some ``infinite constants'' that appear in the renormalisation procedure disappear on the level of Freidlin-Wentzell type large deviations.