Wall-Crossing Structures, Analyticity, and Resurgence

Research Talk: On resurgent Poisson structures and deformations

8 juin 2023, 17:00

1h

Marilyn and James Simons Conference Center (IHES)

Orateur

David Sauzin (Observatoire de Paris Meudon)

Description

I will review the definition of the algebra A of simple Z-resurgent series and its alien derivations ${\mathrm{\Delta }}_m$, as given by Jean Ecalle in 1981. In particular, I will recall why one can say that the alien derivations are independent in a strong sense. Then I will explore one consequence of the freeness of the Lie algebra generated by the ${\mathrm{\Delta }}_m$'s under commutators and multiplication by elements of A: since we have so many derivations (although we are dealing with a formal series of one variable), one can construct non-trivial Poisson structures on A and, correspondingly, non-commutative deformations of
the product of A.

Documents de présentation

Vidéo