ICERM Workshop: Combinatorics, Multiple Dirichlet series and Analytic Number Theory
Recent years have seen a flurry of activity in the field of Weyl group multiple Dirichlet series. Surprising and unexpected connections between these multiple Dirichlet series and several different fields of mathematics have emerged. This workshop will survey recent results and set the stage for future developments which further interrelate analytic number theory, automorphic forms and combinatorial representation theory.
Particular focus will be given to applications of Weyl group multiple Dirichlet series to the following areas:
-Average value and nonvanishing results for families of L-functions
-Periods of automorphic forms
-Connections between characters sums over function fields and characters of affine root systems
-Metaplectic Casselman-Shalika formulae and deformations of the Weyl character formula