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Ranks of Elliptic Curves and Random Matrix Theory
This comprehensive volume introduces elliptic curves and the fundamentals of modeling by a family of random matrices.
Arithmetic and Geometry
The world's leading authorities describe the state of the art in Serre's conjecture and rational points on algebraic varieties.
Surveys in Combinatorics 2015
This book contains surveys of recent important developments in combinatorics covering a wide range of areas in the field.
Inequalities for Graph Eigenvalues
This book explores the inequalities for eigenvalues of the six matrices associated with graphs. Includes the main results and selected applications.
Groups St Andrews 2013
Leading researchers survey the latest developments in group theory and many related areas.
Circuit Double Cover of Graphs
The famous Circuit Double Cover conjecture (and its numerous variants) is considered one of the major open problems in graph theory owing to its close relationship with topological graph theory, integer flow theory, graph coloring and the structure of snarks. It is easy to state: every 2-connected graph has a family of circuits covering every edge precisely twice. C.-Q. Zhang provides an up-to-date overview of the subject containing all of the techniques, methods and results developed to help solve the conjecture since the first publication of the subject in the 1940s. It is a useful survey for researchers already working on the problem and a fitting introduction for those just entering the field. The end-of-chapter exercises have been designed to challenge readers at every level and hints are provided in an appendix.
Elliptic Cohomology
First collection of papers on elliptic cohomology in twenty years; represents the diversity of topics within this important field.
The Cauchy Problem for Non-Lipschitz Semi-Linear Parabolic Partial Differential Equations
A monograph containing significant new developments in the theory of reaction-diffusion systems, particularly those arising in chemistry and life sciences.
Torsors, Étale Homotopy and Applications to Rational Points
Torsors, also known as principal bundles or principal homogeneous spaces, are ubiquitous in mathematics. The purpose of this book is to present expository lecture notes and cutting-edge research papers on the theory and applications of torsors and étale homotopy, all written from different perspectives by leading experts. Part one of the book contains lecture notes on recent uses of torsors in geometric invariant theory and representation theory, plus an introduction to the étale homotopy theory of Artin and Mazur. Part two of the book features a milestone paper on the étale homotopy approach to the arithmetic of rational points. Furthermore, the reader will find a collection of research articles on algebraic groups and homogeneous spaces, rational and K3 surfaces, geometric invariant theory, rational points, descent and the Brauer–Manin obstruction. Together, these give a state-of-the-art view of a broad area at the crossroads of number theory and algebraic geometry.
Geometric and Cohomological Methods in Group Theory
An extended tour through a selection of the most important trends in modern geometric group theory.
