A multiindex-based regularity structure for quasilinear SPDEs

Pablo Linares (MPI MiS Leipzig)

Nov 11. 2021, 14:15 — 14:40

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.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Higher Structures Emerging from Renormalisation (Graduate School)
Pierre Clavier (U of Haut-Alsace)
Kurusch Ebrahimi-Fard (NTNU, Trondheim)
Peter K. Friz (TU Berlin)
Harald Grosse (U of Vienna)
Dominique Manchon (U Clerment Auvergne)
Sylvie Paycha (U of Potsdam)
Sylke Pfeiffer (U of Potsdam)