Algebra/Topology seminar

Speaker: Florian Naef (MIT)

Title: The Goldman-Turaev Lie bialgebra and the Kashiwara-Vergne problem

Abstract: 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, and hence to the theory of Drinfeld associators. Motivated by this result a generalization of the Kashiwara-Vergne problem in higher genera is proposed and shown have solutions. Moreover, an interpretation of the Turaev cobracket on the character variety is proposed, and a higher dimensional string topological analogue is discussed.