Series: London Mathematical Society Lecture Note Series (No. 346)
Paperback (ISBN-13: 9780521698238)
This volume contains survey articles based on the invited lectures given at the Twenty-first British Combinatorial Conference, held in July 2007 at the University of Reading. This biennial conference is a well-established international event and the articles are of the high quality that befits the event. By its nature this volume provides an up-to-date overview of current research activity in several areas of combinatorics, ranging from graph theory to current applications of combinatorial mathematics, including efficient approximability of NP-hard optimization problems and cryptographic key management. The authors are some of the world's foremost researchers in their fields, and here they summarize existing results, and give a unique preview of work currently being written up. The book provides a valuable survey of the present state of knowledge in combinatorics. It will be useful to research workers and advanced graduate students, primarily in mathematics but also in computer science, statistics and engineering.
* Contains survey articles based on the invited lectures given at the Twenty-first
British Combinatorial Conference, a well-established international event
* Authors are some of the world's foremost researchers in their fields
and their survey articles cover topics ranging from graph theory to current
applications of combinatorial mathematics
* The volume provides a valuable summary of existing results and a unique
preview of work currently being written up
Contents
Preface; 1. Hereditary and monotone properties of combinatorial structures B. Bollobas; 2. Ordering classes of matrices of 0’s and 1’s R. A. Brualdi; 3. Cycle decompositions of complete graphs D. Bryant; 4. Excluding induced subgraphs M. Chudnovsky and P. Seymour; 5. Designs and topology M. J. Grannell and T. S. Griggs; 6. The number of points on an algebraic curve over a finite field J. W. P. Hirschfeld, G. Korchmaros and F. Torres; 7. On the efficient approximability of constraint satisfaction problems J. Hastad; 8. The combinatorics of cryptographic key establishment K. M. Martin; 9. Bandwidth of graphic matroids F. Mazoit and S. Thomasse.
Series: New Mathematical Monographs (No. 9)
Hardback (ISBN-13: 9780521882682)
There is now much interplay between studies on logarithmic forms and deep aspects of arithmetic algebraic geometry. New light has been shed, for instance, on the famous conjectures of Tate and Shafarevich relating to abelian varieties and the associated celebrated discoveries of Faltings establishing the Mordell conjecture. This book gives an account of the theory of linear forms in the logarithms of algebraic numbers with special emphasis on the important developments of the past twenty-five years. The first part covers basic material in transcendental number theory but with a modern perspective. The remainder assumes some background in Lie algebras and group varieties, and covers, in some instances for the first time in book form, several advanced topics. The final chapter summarises other aspects of Diophantine geometry including hypergeometric theory and the Andre-Oort conjecture. A comprehensive bibliography rounds off this definitive survey of effective methods in Diophantine geometry.
* Destined to be the definitive reference on effective methods in Diophantine
geometry
* First version in book form of important developments of the past twenty-five
years on multiplicity estimates on group varieties
* Much original material including detailed exposition of the fundamental
analytic subgroup theorem and its applications
Contents
Preface. 1. Transcendence origins; 2. Logarithmic forms; 3. Diophantine problems; 4. Commutative algebraic groups; 5. Multiplicity estimates; 6. The analytic subgroup theorem; 7. The quantitative theory; 8. Further aspects of Diophantine geometry; Bibliography; Index.
Series: New Mathematical Monographs (No. 10)
Hardback (ISBN-13: 9780521880220)
Originating with Andreas Floer in the 1980s, Floer homology provides an invariant of three-dimensional manifolds and four-dimensional cobordisms between them. It has proved to be an effective tool in tackling many important problems in three- and four-dimensional geometry and topology. This book provides a comprehensive treatment of Floer homology, based on the Seiberg-Witten equations. After first providing an overview of the results, the authors develop the analytic properties of the Seiberg-Witten equations, assuming only a basic grounding in differential geometry and analysis. The Floer groups of a general three-manifold are then defined, and their properties studied in detail. Two final chapters are devoted to the calculation of Floer groups, and to applications of the theory in topology. Suitable for beginning graduate students and researchers in the field, this book provides the first full discussion of a central part of the study of the topology of manifolds since the mid 1990s.
* First comprehensive treatment of Seiberg-Witten Floer homology
* Offers a clear overview of recent developments in topology originating
from the material presented
* The treatment of underlying techniques will provide students with skills
applicable elsewhere in geometry and topology
Contents
Preface; 1. Outlines; 2. The Seiberg-Witten equations and compactness; 3. Hilbert manifolds and perturbations; 4. Moduli spaces and transversality; 5. Compactness and gluing; 6. Floer homology; 7. Cobordisms and invariance; 8. Non-exact perturbations; 9. Calculations; 10. Further developments; Bibliography; Glossary of notation; Index.
Series: Cambridge Series in Statistical and Probabilistic Mathematics (No. 24)
Hardback (ISBN-13: 9780521854429)
What is a connected network? How much information can it carry? How can you find a particular destination within the network? How do you approach these questions - and others - when the network is random? The analysis of wireless data networks requires a fascinating synthesis of random graph theory, stochastic geometry and percolation theory to provide models for both structure and information flow. This book is the first comprehensive introduction for graduate students and scientists to techniques and problems in the field of spatial random networks. The selection of material is driven by applications arising in engineering, and the treatment is both readable and mathematically rigorous. Though mainly concerned with information-flow-related questions motivated by wireless data networks, the models developed are also of interest in a broader context, ranging from engineering to social networks, biology, and physics.
* Balanced approach: learn the theory as motivated by real applications
* Focus on information flow, the issue at the heart of communication systems
* Active authors at the forefront of research and development
Contents
Preface; 1. Introduction; 2. Phase transitions in infinite networks; 3. Connectivity of finite networks; 4. More on phase transitions; 5. Statistical physics of information flow; 6. Navigation in random networks; Appendix; References; Index