Trace formulas, character sums, and multiple Dirichlet series

Multiple Dirichlet series (MDS) are Dirichlet series in several complex variables mainly used in studying various analytic properties within certain families of automorphic L-functions (e.g., the family of all quadratic twists of a fixed L-function). I will begin by discussing the main motivation for studying these objects, with particular focus on the MDS associated to moments of quadratic Dirichlet L-functions. We have a local-global compatibility, and when the MDS are associated to moments of quadratic L-series, their local components are determined by connecting moments of character sums of hyperelliptic curves of a given genus over finite fields to traces on spaces of automorphic forms - a comparison of Arthur-Selberg and Grothendieck-Lefschetz trace formulas. In particular, I will present a tight connection with the recent work of J. Bergstr\"om, C. Faber and G. van der Geer. (Joint work with V. Pasol)