Harprit Singh
Title: Renormalisation and homogenisation of non-constant coefficient singular SPDEs
Abstract:
As is well understood, renormalisation of singular SPDEs involving non-constant coefficient differential operators requires the use of (diverging) renormalisation functions, thus a-priori resulting in a notion of solution depending on uncountably many parameters.
In the first part of the talk I shall discuss, using as examples the ϕ⁴ d and g-PAM equation, that these renormalisation functions can be chosen to be local functionals of the coefficient field, resulting in a finite dimensional notion of solution with several desirable properties.
In the second part, which is based on joint work with M. Hairer, I shall discuss homogenisation results for these equations. In particular, we observe that the (divergent) counter-terms split into a local ‘small scale’ part as above and an additional ‘large scale’ part involving familiar objects from homogenisation theory.