Explicit construction of Ramanujan bigraphs -- Classifications of Elliptic Fibrations of K3 surfaces -- Classifications of Elliptic Functions of a singular K3 Surface -- Shalika Germs for Sl(n) and Sp(2n) are Motivic -- The Conjectural Relation Between Generalized Shalika Models on SO4n(F) and Symplectic Linear Models on Sp4n(F): A Toy Example -- Bad Reduction of Genus Three Curves with Complex Multiplication -- Symmetries of Rational Functions Arising in Ecalle's Study of Multiple Zeta Values -- On T-Li Coefficients for Rankin-Selberg L-Functions -- Galois Representations and Galois Groups over Q.

Covering topics in graph theory, L-functions, p-adic geometry, Galois representations, elliptic fibrations, genus 3 curves and bad reduction, harmonic analysis, symplectic groups and mould combinatorics, this volume presents a collection of papers covering a wide swath of number theory emerging from the third iteration of the international Women in Numbers conference, “Women in Numbers - Europe” (WINE), held on October 14–18, 2013 at the CIRM-Luminy mathematical conference center in France. While containing contributions covering a wide range of cutting-edge topics in number theory, the volume emphasizes those concrete approaches that make it possible for graduate students and postdocs to begin work immediately on research problems even in highly complex subjects.