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.