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.

Inhalt
Ramanujan graphs in cryptography (A. Costache, B. Feigon, K. Lauter, M. Massierer, A. Puskás).- Cycles in the supersingular l-isogeny graph and corresponding endomorphisms (E. Bank, C. Camacho-Navarro, K. Eisentraeger, T. Morrison, J. Park).- Chabauty-Coleman experiments for genus 3 curves (J.S. Balakrishnan, F. Bianchi, V. Cantoral-Farfán, M. Çiperiani, A. Etropolski).- Weierstrass equations for the elliptic fibrations of a K3 surface (O. Lecacheux).- Newton polygons of cyclic covers of the projective line branched at three points (Wanlin Li, Elena Mantovan, Rachel Pries, Yunqing Tang).- Arboreal representations for rational maps with few critical points (J. Juul, H. Krieger, N. Looper, M. Manes, B. Thompson, L. Walton).- Dessins d'enfants for single-cycle Belyi maps (M. Manes, G. Melamed, B. Tobin).- Multiplicative order and Frobenius symbol for the reductions of number fields (A. Perucca).- Quantam modular forms and singular combinatorial series with distinct roots of unity (A.Folsom, M.-J. Jang, S. Kimport, H. Swisher).