**Fields Institute Communications**

Volume: 60;
2011;
288 pp;
Hardcover

MSC: Primary 11; 14;

Print ISBN: 978-0-8218-5226-2

Product Code: FIC/60

List Price: $113.00

Individual Member Price: $90.40

**Electronic ISBN: 978-1-4704-1781-9
Product Code: FIC/60.E**

List Price: $113.00

Individual Member Price: $90.40

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# WIN—Women in Numbers: Research Directions in Number Theory

Share this page *Edited by *
*Alina-Carmen Cojocaru; Kristin Lauter; Rachel Pries; Renate Scheidler*

A co-publication of the AMS and Fields Institute

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.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

#### Table of Contents

# Table of Contents

## WIN -- Women in Numbers: Research Directions in Number Theory

- Cover Cover11
- Title page i2
- Contents iii4
- Preface v6
- Part I. Part I. Moduli spaces and Shimura curves 112
- Hilbert modular variety compositions 314
- Contributions to Shimura curves 1526
- Igusa class polynomials, embeddings of quartic CM fields, and arithmetic intersection theory 3546
- 𝑙-adic étale cohomology of PEL type Shimura varieties with non-trivial coefficients 6172
- Part II. Part II. Curves and Jacobians over finite fields 8596
- Pairings on hyperelliptic curves 8798
- Biased statistics for traces of cyclic 𝑝-fold covers over finite fields 121132
- The ℓ-rank structure of a global function field 145156
- Part III. Part III. Galois covers of function fields in positive characteristic 167178
- A survey of Galois theory of curves in characteristic 𝑝 169180
- Covers of the affine line in positive characteristic with prescribed ramification 193204
- Semi-direct Galois covers of the affine line 201212
- Part IV. Part IV. Zeta functions of graphs 211222
- Looking into a graph theory mirror of number theoretic zetas 213224
- Zeta functions of group based graphs and complexes 225236
- Ramified covers of graphs and the Ihara zeta functions of certain ramified covers 237248
- Part V. Part V. Other topics 249260
- Zeros of classical Eisenstein series and recent developments 251262
- On the 𝜇-invariant in Iwasawa theory 265276
- Galois representations and the tame inverse Galois problem 277288
- Back Cover Back Cover1300

#### Readership

Graduate students and research mathematicians interested in number theory.