Research Directions in Number Theory

This is the fifth proceedings volume published under the Women in Numbers umbrella. The WIN workshops and their proceedings volumes are part of the WIN network, aimed at highlighting the research of women and gender minorities in number theory as well as increasing their participation and boosting their potential collaborations in number theory and related fields.

The volume contains research articles in the mathematical area of number theory, written by teams of scholars at all levels in the field. More information about the network, its goals and purpose, past and future conferences, and past proceedings volumes, can be found on the WIN website.

This volume contains research outcomes and results produced by the collaborative research groups created under the Women in Numbers V workshop, the 5th in its series. The actual workshop was to take place in 2020 at the Banff International Research Station in Banff, Canada, but could not take place onsite due to COVID. The associated research groups, each consisting of 1-2 leaders and 2-4 junior researchers, were formed nevertheless and their collaborations went ahead in purely virtual form, as well as other papers by author teams for which at least 50% of the authors identify as women or gender minorities. These contributions include original research and survey articles in a wide variety of subareas within number theory. The former present new cutting-edge research that will be of interest to experts in the field, to the benefit of their own research. The survey articles serve as an accessible introduction for graduate students and other readers to areas of number theory that may be outside their area of expertise.

Showcases high-quality research conducted by female number theorists Presents new and original cutting-edge research Includes useful and accessible survey articles

Auteur
Dr. Alina Bucur is an Associate Professor at University of California San Diego. Her research interests are focused on arithmetic statistics. Dr. Bucur received her B.Sc. from University of Bucharest, Romania, and her Ph.D. from Brown University. She is a fellow of the Association for Women in Mathematics (AWM). Dr. Bucur has served as the AWM Meetings Coordinator and a member of the AWM Executive Committee in 2018-2024 and is a member of the steering committee of the Women in Numbers network.
Dr. Wei Ho is an Associate Professor of Mathematics at the University of Michigan and holds a joint appointment between Princeton University and the Institute for Advanced Study. Her research interests are primarily in arithmetic geometry, number theory, and algebraic geometry. Dr. Ho received her PhD from Princeton University. She is a Fellow of the American Mathematical Society, the Director of the Women+ and Mathematics program at the Institute for Advanced Study, and a member of the steering committee of the Women in Numbers network.
Dr. Renate Scheidler is a Professor at the University of Calgary, with a joint appointment in the Department of Mathematics & Statistics and the Department of Computer Science. She received her Master's degree in mathematics from the University of Cologne and her PhD in computer science from the University of Manitoba. Dr. Scheidler's research interests include algorithmic number theory, focusing on computations involving number fields and algebraic curves as well as applications to cryptography. She is a Fellow of the Association for Women in Mathematics,

Contenu
From Fontaine-Mazur Conjecture to Analytic Pro-p-Groups: A Survey (Abdellatif).- Orientations and Cycles in Supersingular Isogeny Graphs (Stange).- Generalized Ramanujan-Sato Series Arising from Modular Forms (Swisher).- Mock Theta Functions and Related Combinatorics (Ballantine).- Transcendental Lattices of Certain Singular K3 Surfaces (Bertin).- Power-Saving Error Terms for the Number of D4-Quartic Extensions over a Number Field Ordered by Discriminant (Lopez).- Dynamical Mahler Measure: a Survey and Some Recent Results (Lalin).- Geometric Decomposition of Abelian Varieties of Order 1 (Kedlaya).- On Marko Type Surfaces over Number Fields and the Arithmetic of Marko Numbers (Sivaraman).- p-Adic Measures for Reciprocals of L-Functions of Totally Real Number Fields (Taha).