Rough paths based on multi-indices and their algebraic renormalization

27.10.2023, 11:00  –  Raum 2.22, Haus 9, Golm
Arbeitsgruppenseminar Analysis

Pablo Linares (Imperial College, London)

Abstract:

Following the approach of Otto et. al., we derive a notion of rough path based on multi-indices suitable for real-valued rough differential equations, and build its associated algebraic renormalization group. The construction is based on well-known results on pre-Lie algebras (Guin-Oudom construction), applied to pre-Lie products that arise from shifting the affine spaces of solutions and equations. We show that these products correspond in the tree-based language to grafting and insertion, respectively.

We will meet in Room 2.22 of the mathematics building (Haus 9). For those who can't come, please contact Sylvie Paycha for the login details.