Women in Numbers 2

Description:

The second Women in Numbers workshop (WIN2) was held November 6-11, 2011, at the Banff International Research Station (BIRS) in Banff, Alberta, Canada. During the workshop, group leaders presented open problems in various areas of number theory, and working groups tackled those problems in collaborations begun at the workshop and continuing long after. This volume collects articles written by participants of WIN2. Survey papers written by project leaders are designed to introduce areas of active research in number theory to advanced graduate students and recent PhDs. Original research articles by the project groups detail their work on the open problems tackled during and after WIN2. Other articles in this volume contain new research on related topics by women number theorists. The articles collected here encompass a wide range of topics in number theory including Galois representations, the Tamagawa number conjecture, arithmetic intersection formulas, Mahler measures, Newton polygons, the Dwork family, elliptic curves, cryptography, and supercongruences. WIN2 and this Proceedings volume are part of the Women in Numbers network, aimed at increasing the visibility of women researchers' contributions to number theory and at increasing the participation of women mathematicians in number theory and related fields. This book is co-published with the Centre de Recherches Mathématiques. Readership Graduate students and research mathematicians interested in number theory.

subjects: Elliptic Curves,  Congresses,  Arithmetical algebraic geometry,  Number theory,  Number theory -- Arithmetic algebraic geometry (Diophantine geometry) -- Elliptic curves over global fields,  Number theory -- Arithmetic algebraic geometry (Diophantine geometry) ---functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture,  Number theory -- Multiplicative number theory -- Asymptotic results on arithmetic functions,  Number theory -- Algebraic number theory: global fields -- PV-numbers and generalizations; other special algebraic numbers; Mahler measure,  Number theory -- Algebraic number theory: global fields -- Quadratic extensions,  Number theory -- Finite fields and commutative rings (number-theoretic aspects) -- Other character sums and Gauss sums,  Number theory -- Computational number theory -- Algorithms; complexity,  Algebraic geometry -- Surfaces and higher-dimensional varieties -- $K3$ surfaces and Enriques surfaces,  Special functions (33-XX deals with the properties of functions as functions) -- Hypergeometric functions -- Generalized hypergeometric series,,  Information and communication, circuits -- Communication, information -- Cryptography,  Curves, algebraic,  Geometry, algebraic,  Arithmetic algebraic geometry (Diophantine geometry),  Elliptic curves over global fields,  -functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture,  Multiplicative number theory,  Asymptotic results on arithmetic functions,  Algebraic number theory: global fields,  PV-numbers and generalizations; other special algebraic numbers; Mahler measure,  Quadratic extensions,  Finite fields and commutative rings (number-theoretic aspects),  Other character sums and Gauss sums,  Computational number theory,  Algorithms; complexity,  Algebraic geometry,  Surfaces and higher-dimensional varieties,  $K3$ surfaces and Enriques surfaces,  Special functions (33-XX deals with the properties of functions as functions),  Hypergeometric functions,  Generalized hypergeometric series,  Information and communication, circuits,  Communication, information,  Cryptography