This volume includes articles spanning several research areas in number theory, such as arithmetic geometry, algebraic number theory, analytic number theory, and applications in cryptography and coding theory. Most of the articles are the results of collaborations started at the 3rd edition of the Women in Numbers Europe (WINE) conference between senior and mid-level faculty, junior faculty, postdocs, and graduate students. The contents of this book should be of interest to graduate students and researchers in number theory.

Autorentext
**Alina Carmen Cojocaru works in number theory, with a focus on problems lying at the intersection of analytic number theory with arithmetic geometry. She is the recipient of the Doctoral Prize conferred by the Canadian Mathematical Society, the Titeica Prize conferred by the Romanian Academy, and the Career Award conferred by the USA National Science Foundation. Currently, Cojocaru is a professor at the University of Illinois at Chicago and a researcher at the Institute of Mathematics "Simion Stoilow" of the Romanian Academy.
Sorina Ionica is an associate professor of Computer Science at the Université de Picardie Jules Verne, France. Ionica's current research is focused on computational number theory and its applications to cryptography. Her published work includes articles in the areas of elliptic curve cryptography, algorithms for small genus curves and combinatorics.
**Elisa Lorenzo García is an associate professor at Université de Rennes 1, France. She is interested in effective methods in number theory and algebraic geometry. She was the president (2017-2019) of the Comission of Women and Mathematics of the RSME (Spanish Math Society), and she is member of the EGMO (European Girls' Math Olympiad) Advisory Board since 2018 and of CIMPA since 2019.

Inhalt
From modular to adic Langlands correspondences for U(1, 1)(Q2/Q): deformations in the non-supercuspidal case" (A. David).- Explicit connections between supersingular isogeny graphs and BruhatTits trees (L. Amorós, A. Lezzi, K. Lauter, C. Martindale, and J. Sotáková).- Semi-regular sequences and other random systems of equations (E. Gorla).- Reduction types of genus-3 curves in a special stratum of their moduli space (A. Somoza).- Constructions of new matroids and designs over Fq (M. Ceria).- The Complexity of MinRank (E. Gorla).- Fields of definition of elliptic fibrations on covers of certain extremal rational elliptic surfaces (C. Salgado).- Integers represented by ternary quadratic forms (D. Schindler).- Construction of Poincaré-type series by generating kernels (L. Smajlovic).- The Hasse norm principle in global function fields (R. Newton).- Asymptotics of class numbers for real quadratic fields (N. Raulf).- Some split symbol algebras of prime degree (D. Savin).