Cohomology of Groups

Author: Kenneth S. Brown
Publisher: Springer Science & Business Media
ISBN: 9781468493276
Release Date: 2012-12-06
Genre: Mathematics

Aimed at second year graduate students, this text introduces them to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of prerequisites. No homological algebra is assumed beyond what is normally learned in a first course in algebraic topology, and the basics of the subject, as well as exercises, are given prior to discussion of more specialized topics.

Manifolds and Differential Geometry

Author: Jeffrey Marc Lee
Publisher: American Mathematical Soc.
ISBN: 9780821848159
Release Date: 2009
Genre: Mathematics

Differential geometry began as the study of curves and surfaces using the methods of calculus. In time, the notions of curve and surface were generalized along with associated notions such as length, volume, and curvature. At the same time the topic has become closely allied with developments in topology. The basic object is a smooth manifold, to which some extra structure has been attached, such as a Riemannian metric, a symplectic form, a distinguished group of symmetries, or a connection on the tangent bundle. This book is a graduate-level introduction to the tools and structures of modern differential geometry. Included are the topics usually found in a course on differentiable manifolds, such as vector bundles, tensors, differential forms, de Rham cohomology, the Frobenius theorem and basic Lie group theory. The book also contains material on the general theory of connections on vector bundles and an in-depth chapter on semi-Riemannian geometry that covers basic material about Riemannian manifolds and Lorentz manifolds. An unusual feature of the book is the inclusion of an early chapter on the differential geometry of hyper-surfaces in Euclidean space. There is also a section that derives the exterior calculus version of Maxwell's equations. The first chapters of the book are suitable for a one-semester course on manifolds. There is more than enough material for a year-long course on manifolds and geometry.

Books in Print

ISBN: STANFORD:36105015915866
Release Date: 1989
Genre: American literature

Brilliant Light in Life and Material Sciences

Author: Vasili Tsakanov
Publisher: Springer Science & Business Media
ISBN: 9781402057243
Release Date: 2007-09-18
Genre: Science

This book contains an excellent overview of the status and highlights of brilliant light facilities and their applications in biology, chemistry, medicine, materials and environmental sciences. Overview papers on diverse fields of research by leading experts are accompanied by the highlights in the near and long-term perspectives of brilliant X-Ray photon beam usage for fundamental and applied research.

Classical and Quantum Cosmology

Author: Gianluca Calcagni
Publisher: Springer
ISBN: 9783319411279
Release Date: 2017-02-02
Genre: Science

This comprehensive textbook is devoted to classical and quantum cosmology, with particular emphasis on modern approaches to quantum gravity and string theory and on their observational imprint. It covers major challenges in theoretical physics such as the big bang and the cosmological constant problem. An extensive review of standard cosmology, the cosmic microwave background, inflation and dark energy sets the scene for the phenomenological application of all the main quantum-gravity and string-theory models of cosmology. Born of the author's teaching experience and commitment to bridging the gap between cosmologists and theoreticians working beyond the established laws of particle physics and general relativity, this is a unique text where quantum-gravity approaches and string theory are treated on an equal footing. As well as introducing cosmology to undergraduate and graduate students with its pedagogical presentation and the help of 45 solved exercises, this book, which includes an ambitious bibliography of about 3500 items, will serve as a valuable reference for lecturers and researchers.

The Geometry of Algebraic Cycles

Author: Reza Akhtar
Publisher: American Mathematical Soc.
ISBN: 9780821851913
Release Date: 2010
Genre: Mathematics

The subject of algebraic cycles has its roots in the study of divisors, extending as far back as the nineteenth century. Since then, and in particular in recent years, algebraic cycles have made a significant impact on many fields of mathematics, among them number theory, algebraic geometry, and mathematical physics. The present volume contains articles on all of the above aspects of algebraic cycles. It also contains a mixture of both research papers and expository articles, so that it would be of interest to both experts and beginners in the field.

Local Cohomology

Author: M. P. Brodmann
Publisher: Cambridge University Press
ISBN: 9780521513630
Release Date: 2012-11-15
Genre: Mathematics

This second edition of a successful graduate text provides a careful and detailed algebraic introduction to Grothendieck's local cohomology theory, including in multi-graded situations, and provides many illustrations of the theory in commutative algebra and in the geometry of quasi-affine and quasi-projective varieties. Topics covered include Serre's Affineness Criterion, the Lichtenbaum-Hartshorne Vanishing Theorem, Grothendieck's Finiteness Theorem and Faltings' Annihilator Theorem, local duality and canonical modules, the Fulton-Hansen Connectedness Theorem for projective varieties, and connections between local cohomology and both reductions of ideals and sheaf cohomology. The book is designed for graduate students who have some experience of basic commutative algebra and homological algebra and also experts in commutative algebra and algebraic geometry. Over 300 exercises are interspersed among the text; these range in difficulty from routine to challenging, and hints are provided for some of the more difficult ones.

Mathematics Under the Microscope

Author: Alexandre Borovik
Publisher: American Mathematical Soc.
ISBN: 9780821847619
Release Date: 2010
Genre: Mathematics

The author's goal is to start a dialogue between mathematicians and cognitive scientists. He discusses, from a working mathematician's point of view, the mystery of mathematical intuition: why are certain mathematical concepts more intuitive than others? To what extent does the ``small scale'' structure of mathematical concepts and algorithms reflect the workings of the human brain? What are the ``elementary particles'' of mathematics that build up the mathematical universe? The book is saturated with amusing examples from a wide range of disciplines--from turbulence to error-correcting codes to logic--as well as with just puzzles and brainteasers. Despite the very serious subject matter, the author's approach is lighthearted and entertaining. This is an unusual and unusually fascinating book. Readers who never thought about mathematics after their school years will be amazed to discover how many habits of mind, ideas, and even material objects that are inherently mathematical serve as building blocks of our civilization and everyday life. A professional mathematician, reluctantly breaking the daily routine, or pondering on some resisting problem, will open this book and enjoy a sudden return to his or her young days when mathematics was fresh, exciting, and holding all promises. And do not take the word ``microscope'' in the title too literally: in fact, the author looks around, in time and space, focusing in turn on a tremendous variety of motives, from mathematical ``memes'' (genes of culture) to an unusual life of a Hollywood star. --Yuri I. Manin, Max-Planck Institute of Mathematics, Bonn, and Northwestern University

Long Term Studies in Ecology

Author: Gene E. Likens
Publisher: Springer Science & Business Media
ISBN: 9781461573586
Release Date: 2012-12-06
Genre: Science

The Cary Conferences, as we have envisaged them, are different from most scientific meetings in that they provide a forum for major issues in ecology from a more philosophical point of view. It appears to many of us that ecologists have limited opportunities to come together in small groups to address in a more philosophical way some of the major questions and issues that matter very much to the future of humankind and to us as ecologists. Moreover, we hope that the setting ofthe Mary Flagler Cary Arboretum promotes strong interaction and dis cussion between Conference participants with a minimum of distraction. We are proud to make our facilities available for such meetings, and we hope that over the years these Conferences might provide direction and leadership for the whole field of ecology. We have the broad goal of attempting to advance the field of ecology by bringing together leading ecologists and other scientists to address major issues. The first Cary Conference, in 1985, considered the status and future of ecosystem science. This first Conference was rather loosely structured but was successful in stimulating discussion, ideas, and enthusiasm (Likens et al. , 1987). The goals for this second Cary Conference in 1987 were: 1. to identify the roles of long-term studies in ecology; 2. to identify the options for study of long-term ecological phenomena; 3.

Stable Groups

Author: Bruno Poizat
Publisher: American Mathematical Soc.
ISBN: 9780821826850
Release Date: 2001
Genre: Mathematics

This is the English translation of the book originally published in 1987. It is a faithful reproduction of the original, supplemented by a new Foreword and brought up to date by a short postscript. The book gives an introduction by a specialist in contemporary mathematical logic to the model-theoretic study of groups, i.e., into what can be said about groups, and for that matter, about all the traditional algebraic objects. The author introduces the groups of finite Morley rank (those satisfying the most restrictive assumptions from the point of view of logic), and highlights their resemblance to algebraic groups, of which they are the prototypes. (All the necessary prerequisites from algebraic geometry are included in the book.) Then, whenever possible, generalizations of properties of groups of finite Morley type to broader classes of superstables and stable groups are described. The exposition in the first four chapters can be understood by mathematicians who have some knowledge of logic (model theory). The last three chapters are intended for specialists in mathematical logic.

Introduction to Sofic and Hyperlinear Groups and Connes Embedding Conjecture

Author: Valerio Capraro
Publisher: Springer
ISBN: 9783319193335
Release Date: 2015-10-12
Genre: Mathematics

This monograph presents some cornerstone results in the study of sofic and hyperlinear groups and the closely related Connes' embedding conjecture. These notions, as well as the proofs of many results, are presented in the framework of model theory for metric structures. This point of view, rarely explicitly adopted in the literature, clarifies the ideas therein, and provides additional tools to attack open problems. Sofic and hyperlinear groups are countable discrete groups that can be suitably approximated by finite symmetric groups and groups of unitary matrices. These deep and fruitful notions, introduced by Gromov and Radulescu, respectively, in the late 1990s, stimulated an impressive amount of research in the last 15 years, touching several seemingly distant areas of mathematics including geometric group theory, operator algebras, dynamical systems, graph theory, and quantum information theory. Several long-standing conjectures, still open for arbitrary groups, are now settled for sofic or hyperlinear groups. The presentation is self-contained and accessible to anyone with a graduate-level mathematical background. In particular, no specific knowledge of logic or model theory is required. The monograph also contains many exercises, to help familiarize the reader with the topics present.

Xenobiotics in the Soil Environment

Author: Muhammad Zaffar Hashmi
Publisher: Springer
ISBN: 9783319477442
Release Date: 2017-06-16
Genre: Technology & Engineering

This book describes the vast variety of xenobiotics, such as pesticides, antibiotics, antibiotic resistance genes, agrochemicals and other pollutants, their interactions with the soil environment, and the currently available strategies and techniques for soil decontamination and bioremediation. Topics covered include: transport mechanisms of pollutants along the Himalayas; use of earthworms in biomonitoring; metagenomic strategies for assessing contaminated sites; xenobiotics in the food chain; phyto-chemical remediation; biodegradation by fungi; and the use of enzymes and potential microbes in biotransformation. Accordingly, the book offers a valuable guide for scientists in the fields of environmental ecology, soil and food sciences, agriculture, and applied microbiology.