Guillaume Laplante-Anfossi: Operadic structures on genus zero Kashiwara-Vergne solutions

Abstract.

The purpose of this talk will be to show that genus zero Kashiwara-Vergne solutions, as well as their symmetry groups, form colored operads. In this way, one obtains an algebraic "Teichmüller tower" on which the Grothendieck-Teichmüller group acts. The first domino will be a simple linear operad structure on the family of free Lie algebras, which induces another one on their tangential derivations. Among the fruits of this tree-like structure, one recovers Alekseev-Torossian cohomologies as cosimplicial cohomologies of these two operads, and one obtains a short and elegant proof of the fact that KV associators satisfy the pentagon equation. This is ongoing joint work with Zsuzsanna Dancso, Iva Halacheva and Marcy Robertson.