Tree-indexed series, theory and examples I
Seminar Room 1, Newton Institute
To any operad, one can associate a pro-unipotent group much alike the group of formal power series in one variable. This provides a theoretical framework for the use of tree-indexed series in numerical analysis (under the name of Butcher series) by using the PreLie operad. Some examples of tree-indexed series will be presented, with relations to polytopes and Lie idempotents.