## Séminaire de Géométrie et Quantification |

**Matteo
Felder **(Université
de Genève)

Lundi 29 mai à 16h45, salle 01, IHP

*Graph complexes and the Kashiwara-Vergne conjecture.*

Résumé
: The Kashiwara-Vergne Lie algebra *krv2*
was
introduced by A. Alekseev and C. Torossian. It describes the
symmetries of the Kashiwara-Vergne problem in Lie theory. It has been
shown to contain the Grothendieck-Teichmüller Lie algebra *grt*
as
a Lie subalgebra. Conjecturally, these two Lie algebras are expected
to be isomorphic. The aim of this work is to define a nested sequence
of Lie subalgebras of *krv2*
whose
intersection is *grt*.
This infinite family therefore interpolates between the two Lie
algebras. The technical tool used for this construction is the operad
of internally connected graphs ICG introduced by P. Severa and T.
Willwacher. This is joint work with T. Willwacher.