## Séminaire de Géométrie et Quantification |

Florian
Naef

(Genève)

On the
Kashiwara-Vergne problem in higher genera and its connection to the
Goldman-Turaev Lie bialgebra.

Résumé : Using the intersection and self-intersection of
loops on a surface one can define the Goldman-Turaev Lie bialgebra,
and its non-commutative double avatar. On a genus zero surface with
three boundary components the linearization problem of this structure
is equivalent to the Kashiwara-Vergne problem in Lie theory.
Motivated by this result a generalization of the Kashiwara-Vergne
problem in higher genera is proposed and solutions are constructed in
analogy with elliptic associators defined by B. Enriquez. This is
joint work with A. Alekseev, N. Kawazumi and Y. Kuno.

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