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Book DetailsFields Institute CommunicationsVolume: 60; 2011; 288 ppMSC: Primary 11; 14;
This volume is a collection of papers on number theory which evolved out of the workshop WIN—Women In Numbers, held November 2–7, 2008, at the Banff International Research Station (BIRS) in Banff, Alberta, Canada. It includes articles showcasing outcomes from collaborative research initiated during the workshop as well as survey papers aimed at introducing graduate students and recent PhDs to important research topics in number theory.
The contributions in this volume span a wide range of topics in arithmetic geometry and algebraic, algorithmic, and analytic number theory. Clusters of papers center around the four topics of moduli spaces and Shimura curves, curves and Jacobians over finite fields, Galois covers of function fields in positive characteristic, and zeta functions of graphs, with a fifth group of three individual articles on modular forms, Iwasawa theory, and Galois representations, respectively.
The workshop and this volume are part of a broader WIN initiative, whose goals are to highlight and increase the research activities of women in number theory and to train female graduate students in number theory and related fields.ReadershipGraduate students and research mathematicians interested in number theory.
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Table of Contents
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Part I. Moduli spaces and Shimura curves
-
Helen Grundman - Hilbert modular variety compositions
-
Pilar Bayer - Contributions to Shimura curves
-
Helen Grundman, Jennifer Johnson-Leung, Kristin Lauter, Adriana Salerno, Bianca Viray and Erika Wittenborn - Igusa class polynomials, embeddings of quartic CM fields, and arithmetic intersection theory
-
Elena Mantovan - $l$-adic étale cohomology of PEL type Shimura varieties with non-trivial coefficients
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Part II. Curves and Jacobians over finite fields
-
Jennifer Balakrishnan, Juliana Belding, Sarah Chisholm, Kirsten Eisenträger, Katherine Stange and Edlyn Teske - Pairings on hyperelliptic curves
-
Alina Bucur, Chantal David, Brooke Feigon and Matilde Lalín - Biased statistics for traces of cyclic $p$-fold covers over finite fields
-
Lisa Berger, Jing Hoelscher, Yoonjin Lee, Jennifer Paulhus and Renate Scheidler - The $\ell $-rank structure of a global function field
-
Part III. Galois covers of function fields in positive characteristic
-
Rachel Pries and Katherine Stevenson - A survey of Galois theory of curves in characteristic $p$
-
Irene Bouw - Covers of the affine line in positive characteristic with prescribed ramification
-
Linda Gruendken, Laura Hall-Seelig, Bo-Hae Im, Ekin Ozman, Rachel Pries and Katherine Stevenson - Semi-direct Galois covers of the affine line
-
Part IV. Zeta functions of graphs
-
Audrey Terras - Looking into a graph theory mirror of number theoretic zetas
-
Wen-Ching Li - Zeta functions of group based graphs and complexes
-
Beth Malmskog and Michelle Manes - Ramified covers of graphs and the Ihara zeta functions of certain ramified covers
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Part V. Other topics
-
Sharon Garthwaite, Ling Long, Holly Swisher and Stephanie Treneer - Zeros of classical Eisenstein series and recent developments
-
Sujathai Ramdorai - On the $\mu $-invariant in Iwasawa theory
-
Sara Arias-de-Reyna and Núria Vila - Galois representations and the tame inverse Galois problem
-
-
Additional Material
-
RequestsReview Copy – for reviewers who would like to review an AMS bookAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
This volume is a collection of papers on number theory which evolved out of the workshop WIN—Women In Numbers, held November 2–7, 2008, at the Banff International Research Station (BIRS) in Banff, Alberta, Canada. It includes articles showcasing outcomes from collaborative research initiated during the workshop as well as survey papers aimed at introducing graduate students and recent PhDs to important research topics in number theory.
The contributions in this volume span a wide range of topics in arithmetic geometry and algebraic, algorithmic, and analytic number theory. Clusters of papers center around the four topics of moduli spaces and Shimura curves, curves and Jacobians over finite fields, Galois covers of function fields in positive characteristic, and zeta functions of graphs, with a fifth group of three individual articles on modular forms, Iwasawa theory, and Galois representations, respectively.
The workshop and this volume are part of a broader WIN initiative, whose goals are to highlight and increase the research activities of women in number theory and to train female graduate students in number theory and related fields.
Graduate students and research mathematicians interested in number theory.
-
Part I. Moduli spaces and Shimura curves
-
Helen Grundman - Hilbert modular variety compositions
-
Pilar Bayer - Contributions to Shimura curves
-
Helen Grundman, Jennifer Johnson-Leung, Kristin Lauter, Adriana Salerno, Bianca Viray and Erika Wittenborn - Igusa class polynomials, embeddings of quartic CM fields, and arithmetic intersection theory
-
Elena Mantovan - $l$-adic étale cohomology of PEL type Shimura varieties with non-trivial coefficients
-
Part II. Curves and Jacobians over finite fields
-
Jennifer Balakrishnan, Juliana Belding, Sarah Chisholm, Kirsten Eisenträger, Katherine Stange and Edlyn Teske - Pairings on hyperelliptic curves
-
Alina Bucur, Chantal David, Brooke Feigon and Matilde Lalín - Biased statistics for traces of cyclic $p$-fold covers over finite fields
-
Lisa Berger, Jing Hoelscher, Yoonjin Lee, Jennifer Paulhus and Renate Scheidler - The $\ell $-rank structure of a global function field
-
Part III. Galois covers of function fields in positive characteristic
-
Rachel Pries and Katherine Stevenson - A survey of Galois theory of curves in characteristic $p$
-
Irene Bouw - Covers of the affine line in positive characteristic with prescribed ramification
-
Linda Gruendken, Laura Hall-Seelig, Bo-Hae Im, Ekin Ozman, Rachel Pries and Katherine Stevenson - Semi-direct Galois covers of the affine line
-
Part IV. Zeta functions of graphs
-
Audrey Terras - Looking into a graph theory mirror of number theoretic zetas
-
Wen-Ching Li - Zeta functions of group based graphs and complexes
-
Beth Malmskog and Michelle Manes - Ramified covers of graphs and the Ihara zeta functions of certain ramified covers
-
Part V. Other topics
-
Sharon Garthwaite, Ling Long, Holly Swisher and Stephanie Treneer - Zeros of classical Eisenstein series and recent developments
-
Sujathai Ramdorai - On the $\mu $-invariant in Iwasawa theory
-
Sara Arias-de-Reyna and Núria Vila - Galois representations and the tame inverse Galois problem
