Moduli space of flat connections and the Kashiwara-Vergne problem
Speaker: Florian Naef, MIT
Abstract: The moduli space of flat connections on a surface naturally carries a Poisson structure, which can be seen as induced by the intersection of loops on the surface. Also taking self-intersections of loops into consideration one can define the Goldman-Turaev Lie bialgebra structure on the space of loops. On a genus zero surface with three boundary components the linearization problem of this structure is equivalent to the Kashiwara-Vergne problem. 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. This is joint work with Anton Alekseev, Nariya Kawazumi and Yusuke Kuno.
Room Reservation Information
Room Number: 106 McAllister
Time: 2:30pm - 3:30pm