Schedule:

Lecture 1: 3:00pm-5:00pm  December 24, 2024   Room 78301, Jingchunyuan 78, BICMR
Lecture 2: 3:00pm-5:00pm  December 25, 2024   Room 78301, Jingchunyuan 78, BICMR

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). In this mini-course, we will

- give and motivate various definitions concerning moulds (product, exponential, alternality, symmetrality, mould expansions...),
- show how a tiny bit of the mould machinery yields the Baker-Campbell-Hausdorff-Dynkin formula,

- illustrate the use of moulds in the context of alien derivations, 

which are operators acting on a certain subalgebra R of \C[[x]], and in the analysis of linear or nonlinear analytic dynamical systems.