The Kashiwara-Vergne theory

Mercredi 17 octobre 14:00-17:00 - Anton Alekseev - Université de Genève

Résumé : The Duflo Theorem states the isomorphism of the center of the universal enveloping algebra with the ring of invariant polynomials. The Kashiwara-Vergne (KV) problem on the properties of the Baker-Campbell-Hausdorff series is one of the strategies of proving the Duflo Theorem. Surprisingly, it turns out that the KV problem is related to many other fields of mathematics including braid groups, Drinfeld associators and multiple zeta-values.
In this talk, we will start by reviewing the Duflo Theorem and the KV problem, and then we will explain the connection between the KV problem and the Goldman bracket and Turaev cobracket defined by intersections and self-intersections of curves on 2-manifolds. Our toolbox will include the Knizhnik-Zamolodchikov connection and the non-commutative version of the divergence.
The talk is based on joint works with B. Enriquez, N. Kawazumi, Y. Kuno, E. Meinrenken, F. Naef and C. Torossian.

Lieu : Salle 3L8

The Kashiwara-Vergne theory  Version PDF