Contents Preface vii List of Participants ix Automorphic Galois Representations and the Inverse Galois Problem Sara Arias-de-Reyna 1 Two Mayer-Vietoris Spectral Sequences for D-modules Alberto Casta˜ no Dom´ ınguez 17 From Galois to Hopf Galois: Theory and Practice T. Crespo, A. Rio, and M. Vela 29 Elliptic Curves with Torsion Group Z/8Z or Z/2Z × Z/6Z Andrej Dujella and Juan Carlos Peral 47 Equidistribution, L-functions, and Sato-Tate Groups Francesc Fit´ e 63 Covering Techniques and Rational Points on Some Genus 5 Curves Enrique Gonzalez-Jimenez ´ ´ 89 On Quantum Integers and Rationals Bernard Le Stum and Adolfo Quir´ os 107 A Space of Weight 1 Modular Forms Attached to Totally Real Cubic Number Fields Guillermo Mantilla-Soler 131 Characterization of Gaps and Elements of a Numerical Semigroup Using Groebner Bases Guadalupe Marquez-Campos ´ and Jos´ e M. Tornero 139 Classification des repr´ esentations modulaires de GLn(q) en caract´eristique non naturelle Alberto ınguez and Vincent Secherre ´ 163 Fractional p-adic Differentiability Under the Amice Transform Enno Nagel 185 Reciprocity Laws Related to Finite Potent Endomorphisms Fernando Pablos Romo 203 When the Modular World Becomes Non-Holomorphic Dulcinea Raboso 221 v
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