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Explore the algebra of simple Z-resurgent series and its alien derivations in this comprehensive lecture by David Sauzin from Observatoire de Paris Meudon. Delve into Jean Ecalle's 1981 definition of the algebra A and the concept of alien derivations $\Delta_m$, understanding their strong independence. Examine the consequences of the freeness of the Lie algebra generated by the $\Delta_m$'s under commutators and multiplication by elements of A. Discover how this abundance of derivations, despite dealing with formal series of one variable, allows for the construction of non-trivial Poisson structures on A and corresponding non-commutative deformations of the product of A.
