Seminarium Nieliniowość i Geometria

The goal of the talk is to express the extended Goldmansymplectic structure on the $SL(n)$ character variety of a puncturedRiemann surface in terms of Fock-Goncharov coordinates; the associatedsymplectic form has integer coefficients expressed via the inverse ofthe Cartan matrix. The main technical tool is a canonical two-formassociated to a flat graph connection.We discuss the relationship between the extension of the GoldmanPoisson structure and the Poisson structure defined by Fock andGoncharov. We elucidate the role of the Rogers' dilogarithm asgenerating function of the symplectomorpism defined by a graphtransformation. The talk is based on joint work with Dmitri Korotkin.