Pablo Linares - A multiindex-based regularity structure for quasilinear SPDEs

This talk was part of the of the Master Class and Workshop on "Higher Structures Emerging from Renormalisation" held at the ESI November 8 - 19, 2021.

We consider a family of quasilinear SPDEs and parameterize it in terms of the nonlinearity. We use this parameterization to provide an inductive construction of a model, which reveals the algebraic structure of the corresponding model space. We then consider the infinitesimal generators of actions in the space of nonlinearities and use them to build a (pre-)Lie algebra which gives rise to the structure group via its universal envelope. Although the approach is tree-free, we show morphism properties with respect to well-known tree-based structures in branched rough paths and regularity structures. Based on joint work with Felix Otto and Markus Tempelmayr.