Mini-course: A gentle introduction to Mould Calculus (David Sauzin, Paris and Beijing)

12.12.2023 15:00 – 17:00

Abstract:
"Mould Calculus" is a rich combinatorial environment of Hopf-algebraic nature put forward by Jean Écalle since the 1980s. Ultimately, given a commutative ring and a set N, an R-valued mould on N simply consists of
a function from N^r to R for each non-negative integer r ("a function of a variable number of variables"). Mould calculus was initially set up to deal with the infinite-dimensional free associative algebras generated
by alien derivations (another invention of J.Écalle, in the context of Resurgence theory), but its scope goes much beyond—see for instance Écalle's study of Multiple Zeta Values.
We won't touch the latter topic in this mini-course, but rather stay at a more elementary level (ordinary moulds, and no "bimoulds") and content ourselves with
- giving and motivating various definitions concerning moulds (product, exponential, alternality, symmetrality, mould expansions...),
- showing how a tiny bit of the mould machinery yields the Baker-Campbell-Hausdorff-Dynkin formula,
- illustrating the use of moulds in the context of alien derivations, which are operators acting on a certain subalgebra R of \C[[x]].

Lieu

Bâtiment: Conseil Général 7-9

Room 1-07, Tuesday 12.12.2023

entrée libre