Inspired by the September 2016 conference of the same name, this second volume highlights recent research in a wide range of topics in contemporary number theory and arithmetic geometry. Research reports from projects started at the conference, expository papers describing ongoing research, and contributed papers from women number theorists outside the conference make up this diverse volume. Topics cover a broad range of topics such as arithmetic dynamics, failure of local-global principles, geometry in positive characteristics, and heights of algebraic integers. The use of tools from algebra, analysis and geometry, as well as computational methods exemplifies the wealth of techniques available to modern researchers in number theory. Exploring connections between different branches of mathematics and combining different points of view, these papers continue the tradition of supporting and highlighting the contributions of women number theorists at a variety of career stages.Perfect for students and researchers interested in the field, this volume provides an easily accessible introduction and has the potential to inspire future work.

Autorentext

Inhalt

Preface.- Lower bounds for heights in relative Galois Extensions (Shabnam Akhtari, Kevser Aktas¸, Kirsti Biggs, Alia Hamieh, Kathleen Petersen, and Lola Thompson).- Reductions of algebraic integers II (Antonella Perucca).- Reductions of one-dimensional tori II (Antonella Perucca).- On the Carlitz rank of permutation polynomials over finite fields: recent developments (Nurdag¨ul Anbar, Almasa Odzak, Vandita Patel, Luciane Quoos, Anna Somoza, Alev Topuzoglu).- Dynamical Belyi Maps (Jacqueline Anderson, Irene Bouw, Ozlem Ejder, Neslihan Girgin, Valentijn Karemaker, and Michelle Manes).- Discriminant Twins (Alyson Deines).- The a-number of hyperelliptic curves (Sarah Frei).- Non-ordinary curves with a Prym variety of low p-rank (Turku Ozlum Celik, Yara Elias, Burc¸in G¨unes¸, Rachel Newton, Ekin Ozman, Rachel Pries and Lara Thomas).- Elliptic fibrations on covers of the elliptic modular surface of level 5 (Francesca Balestrieri, Julie Desjardins, Alice Garbagnati, C´eline Maistret, Cec´lia Salgado and Isabel Vogt).- On Birch and Swinnerton-Dyer's cubic surfaces (Mckenzie West).