This volume contains a collection of papers on algebraic curves and their applications. While algebraic curves traditionally have provided a path toward modern algebraic geometry, they also provide many applications in number theory, computer security and cryptography, coding theory, differential equations, and more. Papers cover topics such as the rational torsion points of elliptic curves, arithmetic statistics in the moduli space of curves, combinatorial descriptions of semistable hyperelliptic curves over local fields, heights on weighted projective spaces, automorphism groups of curves, hyperelliptic curves, dessins d'enfants, applications to Painlevé equations, descent on real algebraic varieties, quadratic residue codes based on hyperelliptic curves, and Abelian varieties and cryptography. This book will be a valuable resource for people interested in algebraic curves and their connections to other branches of mathematics.
The Hodge Theory of Stable Curves
This textbook uses examples, exercises, diagrams, and unambiguous proof, to help students make the link between classical and differential geometries.
... Mathematical Study of Degenerate Boundary Layers: A Large Scale Ocean Circulation Problem, 2018 Charles Collot, Type II Blow Up Manifolds for the Energy Supercritical Semilinear Wave Equation, 2018 Rui Palma, Crossed Products by Hecke ...
... order terms are of sizes p3/2, p, p1/2, and 1. In every case we are able to analyze, the largest lower order term in the second moment expansion that does not average to zero is on average negative. We prove this “bias conjecture” for ...