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Room P3.10, Mathematics Building

Massimiliano Gubinelli, Oxford University

The flow equation method for singular SPDEs.

In a couple of recent papers Pawel Duch introduced a method to solve singular SPDEs which is based on a description of the solution along a scale parameter and an associated differential equation describing how the SPDE changes along this flow. This method is inspired by the ideas of “renormalization group” and therefore can also be seen as a nice introduction to this framework. In recent work with Paolo Rinaldi we are using this method to control the singularities in the dynamical $\Phi^4_3$ model and its fractional variants towards a stochastic quantisation on the associated invariant measures. In this talk I will try to give an introduction to the various ingredients underlying this construction.