The Ambient Metric Am 178

Author : Charles Fefferman,C. Robin Graham
Publisher : Princeton University Press
Page : 125 pages
File Size : 40,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9780691153148

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The Ambient Metric (AM-178) by Charles Fefferman,C. Robin Graham Pdf

This book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric in n+2 dimensions that encodes a conformal class of metrics in n dimensions. The ambient metric has an alternate incarnation as the Poincaré metric, a metric in n+1 dimensions having the conformal manifold as its conformal infinity. In this realization, the construction has played a central role in the AdS/CFT correspondence in physics. The existence and uniqueness of the ambient metric at the formal power series level is treated in detail. This includes the derivation of the ambient obstruction tensor and an explicit analysis of the special cases of conformally flat and conformally Einstein spaces. Poincaré metrics are introduced and shown to be equivalent to the ambient formulation. Self-dual Poincaré metrics in four dimensions are considered as a special case, leading to a formal power series proof of LeBrun's collar neighborhood theorem proved originally using twistor methods. Conformal curvature tensors are introduced and their fundamental properties are established. A jet isomorphism theorem is established for conformal geometry, resulting in a representation of the space of jets of conformal structures at a point in terms of conformal curvature tensors. The book concludes with a construction and characterization of scalar conformal invariants in terms of ambient curvature, applying results in parabolic invariant theory.

Author : Michael Eastwood,Willard Miller
Publisher : Springer Science & Business Media
Page : 565 pages
File Size : 46,7 Mb
Release : 2009-04-23
Category : Mathematics
ISBN : 9780387738314

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Symmetries and Overdetermined Systems of Partial Differential Equations by Michael Eastwood,Willard Miller Pdf

This three-week summer program considered the symmetries preserving various natural geometric structures. There are two parts to the proceedings. The articles in the first part are expository but all contain significant new material. The articles in the second part are concerned with original research. All articles were thoroughly refereed and the range of interrelated work ensures that this will be an extremely useful collection.

Author : Sigbjørn Hervik,Boris Kruglikov,Irina Markina,Dennis The
Publisher : Springer Nature
Page : 337 pages
File Size : 55,8 Mb
Release : 2022-02-07
Category : Mathematics
ISBN : 9783030812966

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Geometry, Lie Theory and Applications by Sigbjørn Hervik,Boris Kruglikov,Irina Markina,Dennis The Pdf

This book consists of contributions from the participants of the Abel Symposium 2019 held in Ålesund, Norway. It was centered about applications of the ideas of symmetry and invariance, including equivalence and deformation theory of geometric structures, classification of differential invariants and invariant differential operators, integrability analysis of equations of mathematical physics, progress in parabolic geometry and mathematical aspects of general relativity. The chapters are written by leading international researchers, and consist of both survey and research articles. The book gives the reader an insight into the current research in differential geometry and Lie theory, as well as applications of these topics, in particular to general relativity and string theory.

Author : Mauricio Matos Peixoto,Alberto Adrego Pinto,David A. Rand
Publisher : Springer Science & Business Media
Page : 809 pages
File Size : 48,9 Mb
Release : 2011-03-29
Category : Mathematics
ISBN : 9783642114564

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Dynamics, Games and Science I by Mauricio Matos Peixoto,Alberto Adrego Pinto,David A. Rand Pdf

Dynamics, Games and Science I and II are a selection of surveys and research articles written by leading researchers in mathematics. The majority of the contributions are on dynamical systems and game theory, focusing either on fundamental and theoretical developments or on applications to modeling in biology, ecomonics, engineering, finances and psychology. The papers are based on talks given at the International Conference DYNA 2008, held in honor of Mauricio Peixoto and David Rand at the University of Braga, Portugal, on September 8-12, 2008. The aim of these volumes is to present cutting-edge research in these areas to encourage graduate students and researchers in mathematics and other fields to develop them further.

Author : Bob Dziak,Adrienne Copeland,Ana Širovic,DelWayne Roger Bohnenstiehl,Ilse Catharina Van Opzeeland
Publisher : Frontiers Media SA
Page : 287 pages
File Size : 48,8 Mb
Release : 2022-04-04
Category : Science
ISBN : 9782889749188

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Innovation and Discoveries in Marine Soundscape Research by Bob Dziak,Adrienne Copeland,Ana Širovic,DelWayne Roger Bohnenstiehl,Ilse Catharina Van Opzeeland Pdf

Author : Terence Tao
Publisher : American Mathematical Soc.
Page : 206 pages
File Size : 54,9 Mb
Release : 2021-09-03
Category : Education
ISBN : 9781470466404

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An Introduction to Measure Theory by Terence Tao Pdf

This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.

Author : John Voight
Publisher : Springer Nature
Page : 877 pages
File Size : 46,7 Mb
Release : 2021-06-28
Category : Mathematics
ISBN : 9783030566944

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Quaternion Algebras by John Voight Pdf

This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout.

Author : Anonim
Publisher : World Health Organization
Page : 488 pages
File Size : 50,7 Mb
Release : 2010
Category : House & Home
ISBN : UCBK:C105261333

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WHO Guidelines for Indoor Air Quality by Anonim Pdf

This book presents WHO guidelines for the protection of public health from risks due to a number of chemicals commonly present in indoor air. The substances considered in this review, i.e. benzene, carbon monoxide, formaldehyde, naphthalene, nitrogen dioxide, polycyclic aromatic hydrocarbons (especially benzo[a]pyrene), radon, trichloroethylene and tetrachloroethylene, have indoor sources, are known in respect of their hazardousness to health and are often found indoors in concentrations of health concern. The guidelines are targeted at public health professionals involved in preventing health risks of environmental exposures, as well as specialists and authorities involved in the design and use of buildings, indoor materials and products. They provide a scientific basis for legally enforceable standards.

Author : Anonim
Publisher : Unknown
Page : 660 pages
File Size : 44,9 Mb
Release : 1988
Category : Airplanes
ISBN : MINN:30000005882513

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Acceptable Methods, Techniques, and Practices by Anonim Pdf

Author : National Academy of Sciences (U.S.)
Publisher : Unknown
Page : 1080 pages
File Size : 55,7 Mb
Release : 2006
Category : Science
ISBN : WISC:89099178675

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Proceedings of the National Academy of Sciences of the United States of America by National Academy of Sciences (U.S.) Pdf

Author : Loring W. Tu
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 49,6 Mb
Release : 2010-10-05
Category : Mathematics
ISBN : 9781441974006

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An Introduction to Manifolds by Loring W. Tu Pdf

Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.

Author : Boris Khesin,Robert Wendt
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 46,5 Mb
Release : 2008-09-28
Category : Mathematics
ISBN : 9783540772637

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The Geometry of Infinite-Dimensional Groups by Boris Khesin,Robert Wendt Pdf

This monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex geometry. The text includes many exercises and open questions.

Author : Martin R. Bridson,André Häfliger
Publisher : Springer Science & Business Media
Page : 665 pages
File Size : 47,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662124949

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Metric Spaces of Non-Positive Curvature by Martin R. Bridson,André Häfliger Pdf

A description of the global properties of simply-connected spaces that are non-positively curved in the sense of A. D. Alexandrov, and the structure of groups which act on such spaces by isometries. The theory of these objects is developed in a manner accessible to anyone familiar with the rudiments of topology and group theory: non-trivial theorems are proved by concatenating elementary geometric arguments, and many examples are given. Part I provides an introduction to the geometry of geodesic spaces, while Part II develops the basic theory of spaces with upper curvature bounds. More specialized topics, such as complexes of groups, are covered in Part III.

Author : Anonim
Publisher : Unknown
Page : 640 pages
File Size : 42,6 Mb
Release : 1887
Category : Industrial arts
ISBN : NYPL:33433066358775

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English Mechanic and World of Science by Anonim Pdf

Author : Herbert Edelsbrunner,John L. Harer
Publisher : American Mathematical Society
Page : 241 pages
File Size : 51,9 Mb
Release : 2022-01-31
Category : Mathematics
ISBN : 9781470467692

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Computational Topology by Herbert Edelsbrunner,John L. Harer Pdf

Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology. Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. This point of view is critically important in turning a mostly theoretical field of mathematics into one that is relevant to a multitude of disciplines in the sciences and engineering. The main approach is the discovery of topology through algorithms. The book is ideal for teaching a graduate or advanced undergraduate course in computational topology, as it develops all the background of both the mathematical and algorithmic aspects of the subject from first principles. Thus the text could serve equally well in a course taught in a mathematics department or computer science department.