Mathematics : Geometry

This volume contains expositions of many breakthroughs in Kleinian groups and hyperbolic 3-manifolds including Jørgensen's famous paper 'On pairs of once punctured tori'. Graduate students will find much here to inspire them, while established researchers will value this as a snapshot of current research. more...

Price: $68.00

The dense packing of microscopic spheres (i.e. atoms) is the basic geometric arrangement in crystals of mono-atomic elements with weak covalent bonds, which achieves the optimal "known density" of p/√18. In 1611, Johannes Kepler had already "conjectured" that p/√18 should be the optimal "density" of sphere packings. Thus, the central problems in the study of sphere packings are the proof of Kepler's conjecture that p/√18 is the optimal density, and the establishing of the least action principle that the hexagonal dense packings in crystals are the geometric consequence of optimization of density. This important book provides a self-contained proof of both, using vector algebra and spherical geometry as the main techniques and in the tradition of classical geometry. more...

Price: $88.40

Noncommutative geometry provides a powerful tool for regularizing quantum field theories in the form of fuzzy physics. Fuzzy physics maintains symmetries, has no fermion-doubling problem and represents topological features efficiently. These lecture notes provide a comprehensive introduction to the field. Starting with the construction of fuzzy spaces, using the concrete examples of the fuzzy sphere and fuzzy complex projective spaces, the book moves on to discuss the technology of star products on noncommutative R2d and on the fuzzy sphere. Scalar, spinor and gauge field theories as well as extended objects such as monopoles and nonlinear sigma modes are treated in considerable detail. A detailed treatment of the regularization of supersymmetry is given using the techniques of fuzzy physics. more...

Price: $62.40

This book constitutes the refereed proceedings of the 12th IMA International Conference on the Mathematics of Surfaces, held in Sheffield, UK in September 2007. The 22 revised full papers presented together with 8 invited papers were carefully reviewed and selected from numerous submissions. Among the topics addressed is the applicability of various aspects of mathematics to engineering and computer science, especially in domains such as computer aided design, computer vision, and computer graphics. The papers cover a range of ideas from underlying theoretical tools to industrial uses of surfaces. Research is reported on theoretical aspects of surfaces including topology, parameterization, differential geometry, and conformal geometry, and also more practical topics such as geometric tolerances, computing shape from shading, and medial axes for industrial applications. Other specific areas of interest include subdivision schemes, solutions of differential equations on surfaces, knot insertion, surface segmentation, surface deformation, and surface fitting. more...

Price: $89.95

The last half century has seen the development of many biological or physical theories that have explicitly or implicitly involved medial descriptions of objects and other spatial entities in our world. Simultaneously, mathematicians have studied the properties of these skeletal descriptions of shape, and, stimulated by the many areas where medial models are useful, computer scientists and engineers have developed numerous algorithms for computing and using these models. The book consists of an introductory chapter, two chapters on the major mathematical results on medial representations, five chapters on algorithms for extracting medial models from boundary or binary image descriptions of objects, and three chapters on applications in image analysis and other areas of study and design. This book will serve the science and engineering communities using medial models and will provide learning material for students entering this field. more...

Price: $119.00