The aromatic bicomplex for the study of volume-preserving integrators (Adrien Laurent, Bergen)

28.03.2023 14:00

While B-series are used to represent the Taylor expansion of the solution of an ODE, aromatic B-series appear when computing the divergence of such a Taylor expansion. In this talk, we define aromatic forms (in the spirit of differential forms), we extend the divergence operator on aromatic forms, and we introduce the aromatic bicomplex, in the spirit of the variational bicomplex in differential geometry. We prove the exactness of this bicomplex with the help of the Euler and the homotopy operators. We will describe the far-reaching implications of the exactness of the aromatic bicomplex in the study of volume preservation.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Séminaire d'analyse numérique

entrée libre