Abstract: p-adic Whittaker functions on metaplectic groups are the key to constructing interesting multiple Dirichlet series related to the reciprocity laws of number theory. The coefficients of these multiple Dirichlet series have fascinating connections with combinatorics, representation theory, statistical mechanics, and geometry.
About the picture: The image shows the analytic continuation of a double Dirichlet series from the region of absolute convergence (dark gray) to the 2-dimensional complex domain by application of Bochner's convexity principle. Superimposed on this is a Demazure character on a crystal graph, and the Sage command that creates the crystal. This is the logo of the upcoming ICERM Semester Program "Automorphic Forms, Combinatorial Representation Theory and Multiple Dirichlet Series" (January 28, 2013 - May 3, 2013). See http://icerm.brown.edu/sp-s13 for further information.