Weak universality of some singular SPDEs

Formal considerations in mathematical physics often lead to so called “singular stochastic partial differential equations” (singular SPDEs), which have been mathematically ill posed for a long time. The problem is the interplay of very singular noise with nonlinearities, which creates small scale resonances that have be removed through a renormalization procedure. In the past five years we have seen a number of mathematical breakthroughs that allow us to finally solve and study such singular SPDEs. Now that solution theories are available we can rigorously study the predictions by mathematical physicists by proving the so called “weak universality” of these singular SPDEs.