An overview of recent algebraic and numerical results on aromatic structures (Adrien Busnot Laurent, INRIA Rennes)

21.08.2026 15:00

Aromatic Butcher series are the natural extension of the standard B-series that allow to compute the divergence of a Taylor expansion over the jet space of a given ODE. First used as a tool for the study of volume-preserving numerical integrators, they were then studied for their numerous algebraic properties.
In this talk, we will introduce aromatic structures step by step with freeness results and applications. Then, we shall present the aromatic bicomplex, in the spirit of the variational bicomplex in variational calculus, characterise Ker(Div) on aromatic trees, derive negative results on volume-preserving methods, and formulate the notion of symmetries and Noether theorems for tree-like structures. We will extend our approach to the preservation of measures for stochastic dynamics with a focus on the algebraic structure. If time allows, we will give an overview of related algebraic structures, that are aromatic multi-indices, Hopf algebroids, and planar aromatic trees, and discuss how they are used to tackle the open problems of geometric integration concerning measure-preservation.

Lieu

Conseil Général 7-9, Room 1-05, Séminaire d'analyse numérique, ATT: unusual time.

entrée libre