Substitution in Lie-Butcher Series

Ludwig Rahm (NTNU, Trondheim)

Nov 10. 2021, 14:50 — 15:15

The talk will follow an operadic approach to provide a bialgebraic description of substitution for Lie-Butcher series. I will first show how the well-known bialgebraic description for substitution in Butcher's B-series can be obtained from the pre-Lie operad. I will then apply the same construction to the post-Lie operad to arrive at a bialgebra Q. By considering a module over the post-Lie operad, we get a cointeraction between Q and the Hopf algebra H_MKW that describes composition for Lie-Butcher series. This coaction is then used to describe substitution for Lie-Butcher series.

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)