Pre-Lie algebras in stochastic PDEs

Abstract: In this talk, I will discuss a general method to renormalise singular stochastic partial differential equations (SPDEs) using the theory of regularity structures. It turns out that, to derive the renormalised equation, one can employ a convenient multi-pre-Lie algebra. The pre-Lie products in this algebra are reminiscent of the pre-Lie product on the Grossman-Larson algebra of trees, but come with several important twists. For the renormalisation of SPDEs, the important feature of this multi-pre-Lie algebra is that it is free in a certain sense. Based on joint work with Yvain Bruned, Ajay Chandra, and Martin Hairer.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar