Research Directions in Number Theory: Women in Numbers IV

Description

These proceedings collect several number theory articles, most of which were written in connection to the workshop WIN4: Women in Numbers, held in August 2017, at the Banff International Research Station (BIRS) in Banff, Alberta, Canada. It collects papers disseminating research outcomes from collaborations initiated during the workshop as well as other original research contributions involving participants of the WIN workshops. The workshop and this volume 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. Front Matter ....Pages i-xix Ramanujan Graphs in Cryptography (Anamaria Costache, Brooke Feigon, Kristin Lauter, Maike Massierer, Anna Puskás)....Pages 1-40 Cycles in the Supersingular ℓ-Isogeny Graph and Corresponding Endomorphisms (Efrat Bank, Catalina Camacho-Navarro, Kirsten Eisenträger, Travis Morrison, Jennifer Park)....Pages 41-66 Chabauty–Coleman Experiments for Genus 3 Hyperelliptic Curves (Jennifer S. Balakrishnan, Francesca Bianchi, Victoria Cantoral-Farfán, Mirela Çiperiani, Anastassia Etropolski)....Pages 67-90 Weierstrass Equations for the Elliptic Fibrations of a K3 Surface (Odile Lecacheux)....Pages 91-114 Newton Polygons of Cyclic Covers of the Projective Line Branched at Three Points (Wanlin Li, Elena Mantovan, Rachel Pries, Yunqing Tang)....Pages 115-132 Arboreal Representations for Rational Maps with Few Critical Points (Jamie Juul, Holly Krieger, Nicole Looper, Michelle Manes, Bianca Thompson, Laura Walton)....Pages 133-151 Dessins D’enfants for Single-Cycle Belyi Maps (Michelle Manes, Gabrielle Melamed, Bella Tobin)....Pages 153-159 Multiplicative Order and Frobenius Symbol for the Reductions of Number Fields (Antonella Perucca)....Pages 161-171 Quantum Modular Forms and Singular Combinatorial Series with Distinct Roots of Unity (Amanda Folsom, Min-Joo Jang, Sam Kimport, Holly Swisher)....Pages 173-195