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1-20 21-27

    Nguyen-Schäfer, Hung.
    Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers [Electronic resource] / Hung. Nguyen-Schäfer, Schmidt, Jan-Philip. ; . - 2nd ed. 2017. - [S. l. : s. n.]. - XVII, 376 p. 73 illus. - ISBN 9783662484975
    Зміст:

Рубрики: Engineering mathematics.
   Differential geometry.
   Physics.
   Computer mathematics.
   Engineering Mathematics.
   Differential Geometry.
   Mathematical Methods in Physics.
   Computational Science and Engineering.
Анотація: This book comprehensively presents topics, such as Dirac notation, tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. Additionally, two new chapters of Cartan differential forms and Dirac and tensor notations in quantum mechanics are added to this second edition. The reader is provided with hands-on calculations and worked-out examples at which he will learn how to handle the bra-ket notation, tensors, differential geometry, and differential forms; and to apply them to the physical and engineering world. Many methods and applications are given in CFD, continuum mechanics, electrodynamics in special relativity, cosmology in the Minkowski four-dimensional spacetime, and relativistic and non-relativistic quantum mechanics. Tensors, differential geometry, differential forms, and Dirac notation are very useful advanced mathematical tools in many fields of modern physics and computational engineering. They are involved in special and general relativity physics, quantum mechanics, cosmology, electrodynamics, computational fluid dynamics (CFD), and continuum mechanics. The target audience of this all-in-one book primarily comprises graduate students in mathematics, physics, engineering, research scientists, and engineers. .
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Schmidt, Jan-Philip.; Nguyen-Schäfer, Hung. \.\
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    Algebra, Geometry, and Physics in the 21st Century [Electronic resource] : kontsevich Festschrift / / ed. Auroux, Denis. [et al.]. - 1st ed. 2017. - [S. l. : s. n.]. - VII, 364 p. 65 illus., 40 illus. in color. - ISBN 9783319599397
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Рубрики: Algebraic geometry.
   Differential geometry.
   Category theory (Mathematics).
   Homological algebra.
   Algebraic Geometry.
   Differential Geometry.
   Category Theory, Homological Algebra.
Анотація: This volume is a tribute to Maxim Kontsevich, one of the most original and influential mathematicians of our time. Maxim’s vision has inspired major developments in many areas of mathematics, ranging all the way from probability theory to motives over finite fields, and has brought forth a paradigm shift at the interface of modern geometry and mathematical physics. Many of his papers have opened completely new directions of research and led to the solutions of many classical problems. This book collects papers by leading experts currently engaged in research on topics close to Maxim’s heart. Contributors: S. Donaldson A. Goncharov D. Kaledin M. Kapranov A. Kapustin L. Katzarkov A. Noll P. Pandit S. Pimenov J. Ren P. Seidel C. Simpson Y. Soibelman R. Thorngren.
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Auroux, Denis. \ed.\; Katzarkov, Ludmil. \ed.\; Pantev, Tony. \ed.\; Soibelman, Yan. \ed.\; Tschinkel, Yuri. \ed.\
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    Topics in Modern Differential Geometry [Electronic resource] / ed.: Haesen, Stefan., Verstraelen, Leopold. - 1st ed. 2017. - [S. l. : s. n.]. - VII, 284 p. 30 illus., 4 illus. in color. - ISBN 9789462392403
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Рубрики: Differential geometry.
Differential Geometry.
Анотація: A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.
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Haesen, Stefan. \ed.\; Verstraelen, Leopold. \ed.\
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    Innovative Algorithms and Analysis [Electronic resource] / ed.: Gosse, Laurent., Natalini, Roberto. - 1st ed. 2017. - [S. l. : s. n.]. - XVIII, 351 p. 70 illus., 60 illus. in color. - ISBN 9783319492629
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Рубрики: Applied mathematics.
   Engineering mathematics.
   Partial differential equations.
   Computer mathematics.
   Biomathematics.
   Differential geometry.
   Physics.
   Applications of Mathematics.
   Partial Differential Equations.
   Computational Mathematics and Numerical Analysis.
   Mathematical and Computational Biology.
   Differential Geometry.
   Mathematical Methods in Physics.
Анотація: This volume gathers contributions reflecting topics presented during an INDAM workshop held in Rome in May 2016. The event brought together many prominent researchers in both Mathematical Analysis and Numerical Computing, the goal being to promote interdisciplinary collaborations. Accordingly, the following thematic areas were developed: 1. Lagrangian discretizations and wavefront tracking for synchronization models; 2. Astrophysics computations and post-Newtonian approximations; 3. Hyperbolic balance laws and corrugated isometric embeddings; 4. “Caseology” techniques for kinetic equations; 5. Tentative computations of compressible non-standard solutions; 6. Entropy dissipation, convergence rates and inverse design issues. Most of the articles are presented in a self-contained manner; some highlight new achievements, while others offer snapshots of the “state of the art” in certain fields. The book offers a unique resource, both for young researchers looking to quickly enter a given area of application, and for more experienced ones seeking comprehensive overviews and extensive bibliographic references.
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Gosse, Laurent. \ed.\; Natalini, Roberto. \ed.\
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    Lorentzian Geometry and Related Topics [Electronic resource] : geLoMa 2016, Málaga, Spain, September 20–23 / / ed.: Cañadas-Pinedo, María A., Flores, José Luis., Palomo, Francisco J. - 1st ed. 2017. - [S. l. : s. n.]. - X, 273 p. 14 illus., 8 illus. in color. - ISBN 9783319662909
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Рубрики: Differential geometry.
   Gravitation.
   Differential Geometry.
   Classical and Quantum Gravitation, Relativity Theory.
Анотація: This volume contains a collection of research papers and useful surveys by experts in the field which provide a representative picture of the current status of this fascinating area. Based on contributions from the VIII International Meeting on Lorentzian Geometry, held at the University of Málaga, Spain, this volume covers topics such as distinguished (maximal, trapped, null, spacelike, constant mean curvature, umbilical...) submanifolds, causal completion of spacetimes, stationary regions and horizons in spacetimes, solitons in semi-Riemannian manifolds, relation between Lorentzian and Finslerian geometries and the oscillator spacetime. In the last decades Lorentzian geometry has experienced a significant impulse, which has transformed it from just a mathematical tool for general relativity to a consolidated branch of differential geometry, interesting in and of itself. Nowadays, this field provides a framework where many different mathematical techniques arise with applications to multiple parts of mathematics and physics. This book is addressed to differential geometers, mathematical physicists and relativists, and graduate students interested in the field.
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Cañadas-Pinedo, María A. \ed.\; Flores, José Luis. \ed.\; Palomo, Francisco J. \ed.\
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    Pseudo-Differential Operators: Groups, Geometry and Applications [Electronic resource] / ed.: Wong, M. W., Zhu, Hongmei. - 1st ed. 2017. - [S. l. : s. n.]. - VIII, 239 p. 23 illus., 11 illus. in color. - ISBN 9783319475127
    Зміст:

Рубрики: Operator theory.
   Partial differential equations.
   Differential geometry.
   Probabilities.
   Information theory.
   Operator Theory.
   Partial Differential Equations.
   Differential Geometry.
   Probability Theory and Stochastic Processes.
   Information and Communication, Circuits.
Анотація: This volume consists of papers inspired by the special session on pseudo-differential operators at the 10th ISAAC Congress held at the University of Macau, August 3-8, 2015 and the mini-symposium on pseudo-differential operators in industries and technologies at the 8th ICIAM held at the National Convention Center in Beijing, August 10-14, 2015. The twelve papers included present cutting-edge trends in pseudo-differential operators and applications from the perspectives of Lie groups (Chapters 1-2), geometry (Chapters 3-5) and applications (Chapters 6-12). Many contributions cover applications in probability, differential equations and time-frequency analysis. A focus on the synergies of pseudo-differential operators with applications, especially real-life applications, enhances understanding of the analysis and the usefulness of these operators.
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Wong, M. W. \ed.\; Zhu, Hongmei. \ed.\
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    Walczak, Szymon M.
    Metric Diffusion Along Foliations [Electronic resource] / Szymon M. Walczak ; . - 1st ed. 2017. - [S. l. : s. n.]. - XI, 55 p. 19 illus. - ISBN 9783319575179
    Зміст:

Рубрики: Topology.
   Differential geometry.
   Topology.
   Differential Geometry.
Анотація: Up-to-date research in metric diffusion along compact foliations is presented in this book. Beginning with fundamentals from the optimal transportation theory and the theory of foliations; this book moves on to cover Wasserstein distance, Kantorovich Duality Theorem, and the metrization of the weak topology by the Wasserstein distance. Metric diffusion is defined, the topology of the metric space is studied and the limits of diffused metrics along compact foliations are discussed. Essentials on foliations, holonomy, heat diffusion, and compact foliations are detailed and vital technical lemmas are proved to aide understanding. Graduate students and researchers in geometry, topology and dynamics of foliations and laminations will find this supplement useful as it presents facts about the metric diffusion along non-compact foliation and provides a full description of the limit for metrics diffused along foliation with at least one compact leaf on the two dimensions.
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Walczak, Szymon M. \.\
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    Löh, Clara.
    Geometric Group Theory [Electronic resource] : an Introduction / / Clara. Löh ; . - 1st ed. 2017. - [S. l. : s. n.]. - XI, 389 p. 119 illus., 100 illus. in color. - ISBN 9783319722542
    Зміст:

Рубрики: Group theory.
   Differential geometry.
   Hyperbolic geometry.
   Manifolds (Mathematics).
   Complex manifolds.
   Graph theory.
   Group Theory and Generalizations.
   Differential Geometry.
   Hyperbolic Geometry.
   Manifolds and Cell Complexes (incl. Diff.Topology).
   Graph Theory.
Анотація: Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.
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Löh, Clara. \.\
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    Ay, Nihat.
    Information Geometry [Electronic resource] / Nihat. Ay, Jost, Jürgen., Lê, Hông Vân., Schwachhöfer, Lorenz. ; . - 1st ed. 2017. - [S. l. : s. n.]. - XI, 407 p. 15 illus. - ISBN 9783319564784
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Рубрики: Statistics .
   Data structures (Computer science).
   Differential geometry.
   Convex geometry .
   Discrete geometry.
   Functional analysis.
   System theory.
   Statistical Theory and Methods.
   Data Structures.
   Differential Geometry.
   Convex and Discrete Geometry.
   Functional Analysis.
   Complex Systems.
Анотація: The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, information theory, or the foundations of statistics, to statisticians as well as to scientists interested in the mathematical foundations of complex systems.
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Jost, Jürgen.; Lê, Hông Vân.; Schwachhöfer, Lorenz.; Ay, Nihat. \.\
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10.

    Ergodic Theory and Negative Curvature [Electronic resource] : CIRM Jean-Morlet Chair, Fall 2013 / / ed. Hasselblatt, Boris. - 1st ed. 2017. - [S. l. : s. n.]. - VII, 328 p. 68 illus., 17 illus. in color. - ISBN 9783319430591
Рубрики: Dynamics.
   Ergodic theory.
   Differential geometry.
   Dynamical Systems and Ergodic Theory.
   Differential Geometry.
Анотація: Focussing on the mathematics related to the recent proof of ergodicity of the (Weil–Petersson) geodesic flow on a nonpositively curved space whose points are negatively curved metrics on surfaces, this book provides a broad introduction to an important current area of research. It offers original textbook-level material suitable for introductory or advanced courses as well as deep insights into the state of the art of the field, making it useful as a reference and for self-study. The first chapters introduce hyperbolic dynamics, ergodic theory and geodesic and horocycle flows, and include an English translation of Hadamard's original proof of the Stable-Manifold Theorem. An outline of the strategy, motivation and context behind the ergodicity proof is followed by a careful exposition of it (using the Hopf argument) and of the pertinent context of Teichmüller theory. Finally, some complementary lectures describe the deep connections between geodesic flows in negative curvature and Diophantine approximation.
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Hasselblatt, Boris. \ed.\
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11.

    Developments in Functional Equations and Related Topics [Electronic resource] / ed.: Brzdęk, Janusz., Ciepliński, Krzysztof., Rassias, Themistocles M. - 1st ed. 2017. - [S. l. : s. n.]. - XII, 352 p. 2 illus. - ISBN 9783319617329
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Рубрики: Difference equations.
   Functional equations.
   Approximation theory.
   Differential geometry.
   Functional analysis.
   Probabilities.
   Difference and Functional Equations.
   Approximations and Expansions.
   Differential Geometry.
   Functional Analysis.
   Probability Theory and Stochastic Processes.
Анотація: This book presents current research on Ulam stability for functional equations and inequalities. Contributions from renowned scientists emphasize fundamental and new results, methods and techniques. Detailed examples are given to theories to further understanding at the graduate level for students in mathematics, physics, and engineering. Key topics covered in this book include: Quasi means Approximate isometries Functional equations in hypergroups Stability of functional equations Fischer-Muszély equation Haar meager sets and Haar null sets Dynamical systems Functional equations in probability theory Stochastic convex ordering Dhombres functional equation Nonstandard analysis and Ulam stability This book is dedicated in memory of Staniłsaw Marcin Ulam, who posed the fundamental problem concerning approximate homomorphisms of groups in 1940; which has provided the stimulus for studies in the stability of functional equations and inequalities.
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Brzdęk, Janusz. \ed.\; Ciepliński, Krzysztof. \ed.\; Rassias, Themistocles M. \ed.\
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12.

    Wells, Jr. , Raymond O.
    Differential and Complex Geometry: Origins, Abstractions and Embeddings [Electronic resource] / Jr. , Raymond O. Wells ; . - 1st ed. 2017. - [S. l. : s. n.]. - XIV, 319 p. 47 illus., 18 illus. in color. - ISBN 9783319581842
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Рубрики: Differential geometry.
   Global analysis (Mathematics).
   Manifolds (Mathematics).
   Functions of complex variables.
   Projective geometry.
   Algebraic topology.
   Differential Geometry.
   Global Analysis and Analysis on Manifolds.
   Several Complex Variables and Analytic Spaces.
   Projective Geometry.
   Algebraic Topology.
Анотація: Differential and complex geometry are two central areas of mathematics with a long and intertwined history. This book, the first to provide a unified historical perspective of both subjects, explores their origins and developments from the sixteenth to the twentieth century. Providing a detailed examination of the seminal contributions to differential and complex geometry up to the twentieth century embedding theorems, this monograph includes valuable excerpts from the original documents, including works of Descartes, Fermat, Newton, Euler, Huygens, Gauss, Riemann, Abel, and Nash. Suitable for beginning graduate students interested in differential, algebraic or complex geometry, this book will also appeal to more experienced readers.
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Wells, Jr., Raymond O. \.\
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13.

    Special Metrics and Group Actions in Geometry [Electronic resource] / ed. Chiossi, Simon G. [et al.]. - 1st ed. 2017. - [S. l. : s. n.]. - X, 338 p. 12 illus., 11 illus. in color. - ISBN 9783319675190
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Рубрики: Topological groups.
   Lie groups.
   Differential geometry.
   Global analysis (Mathematics).
   Manifolds (Mathematics).
   Algebraic geometry.
   Topological Groups, Lie Groups.
   Differential Geometry.
   Global Analysis and Analysis on Manifolds.
   Algebraic Geometry.
Анотація: The volume is a follow-up to the INdAM meeting “Special metrics and quaternionic geometry” held in Rome in November 2015. It offers a panoramic view of a selection of cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and octonionic geometry, twistor spaces, harmonic maps, spinors, complex and conformal geometry, homogeneous spaces and nilmanifolds, special geometries in dimensions 5–8, gauge theory, symplectic and toric manifolds, exceptional holonomy and integrable systems. The workshop was held in honor of Simon Salamon, a leading international scholar at the forefront of academic research who has made significant contributions to all these subjects. The articles published here represent a compelling testimony to Salamon’s profound and longstanding impact on the mathematical community. Target readership includes graduate students and researchers working in Riemannian and complex geometry, Lie theory and mathematical physics.
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Chiossi, Simon G. \ed.\; Fino, Anna. \ed.\; Musso, Emilio. \ed.\; Podestà, Fabio. \ed.\; Vezzoni, Luigi. \ed.\
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14.

    Tu, Loring W.
    Differential Geometry [Electronic resource] : connections, Curvature, and Characteristic Classes / / Loring W. Tu ; . - 1st ed. 2017. - [S. l. : s. n.]. - XVII, 347 p. 87 illus., 15 illus. in color. - ISBN 9783319550848
    Зміст:

Рубрики: Differential geometry.
   Algebraic geometry.
   Differential Geometry.
   Algebraic Geometry.
Анотація: This text presents a graduate-level introduction to differential geometry for mathematics and physics students. The exposition follows the historical development of the concepts of connection and curvature with the goal of explaining the Chern–Weil theory of characteristic classes on a principal bundle. Along the way we encounter some of the high points in the history of differential geometry, for example, Gauss' Theorema Egregium and the Gauss–Bonnet theorem. Exercises throughout the book test the reader’s understanding of the material and sometimes illustrate extensions of the theory. Initially, the prerequisites for the reader include a passing familiarity with manifolds. After the first chapter, it becomes necessary to understand and manipulate differential forms. A knowledge of de Rham cohomology is required for the last third of the text. Prerequisite material is contained in author's text An Introduction to Manifolds, and can be learned in one semester. For the benefit of the reader and to establish common notations, Appendix A recalls the basics of manifold theory. Additionally, in an attempt to make the exposition more self-contained, sections on algebraic constructions such as the tensor product and the exterior power are included. Differential geometry, as its name implies, is the study of geometry using differential calculus. It dates back to Newton and Leibniz in the seventeenth century, but it was not until the nineteenth century, with the work of Gauss on surfaces and Riemann on the curvature tensor, that differential geometry flourished and its modern foundation was laid. Over the past one hundred years, differential geometry has proven indispensable to an understanding of the physical world, in Einstein's general theory of relativity, in the theory of gravitation, in gauge theory, and now in string theory. Differential geometry is also useful in topology, several complex variables, algebraic geometry, complex manifolds, and dynamical systems, among other fields. The field has even found applications to group theory as in Gromov's work and to probability theory as in Diaconis's work. It is not too far-fetched to argue that differential geometry should be in every mathematician's arsenal.
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Tu, Loring W. \.\
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15.

    Towards a Theory of Spacetime Theories [Electronic resource] / ed.: Lehmkuhl, Dennis., Schiemann, Gregor., Scholz, Erhard. - 1st ed. 2017. - [S. l. : s. n.]. - VIII, 335 p. 7 illus. - ISBN 9781493932108
    Зміст:

Рубрики: Mathematics.
   History.
   Mathematical physics.
   Differential geometry.
   History of Mathematical Sciences.
   Theoretical, Mathematical and Computational Physics.
   Mathematical Physics.
   Differential Geometry.
Анотація: This contributed volume is the result of a July 2010 workshop at the University of Wuppertal Interdisciplinary Centre for Science and Technology Studies which brought together world-wide experts from physics, philosophy and history, in order to address a set of questions first posed in the 1950s: How do we compare spacetime theories? How do we judge, objectively, which is the “best” theory? Is there even a unique answer to this question? The goal of the workshop, and of this book, is to contribute to the development of a meta-theory of spacetime theories. Such a meta-theory would reveal insights about specific spacetime theories by distilling their essential similarities and differences, deliver a framework for a class of theories that could be helpful as a blueprint to build other meta-theories, and provide a higher level viewpoint for judging which theory most accurately describes nature. But rather than drawing a map in broad strokes, the focus is on particularly rich regions in the “space of spacetime theories.” This work will be of interest to physicists, as well as philosophers and historians of science working with or interested in General Relativity and/or Space, Time and Gravitation more generally.
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Lehmkuhl, Dennis. \ed.\; Schiemann, Gregor. \ed.\; Scholz, Erhard. \ed.\
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16.

    Analytic, Algebraic and Geometric Aspects of Differential Equations [Electronic resource] : będlewo, Poland, September 2015 / / ed.: Filipuk, Galina., Haraoka, Yoshishige., Michalik, Sławomir. - 1st ed. 2017. - [S. l. : s. n.]. - VIII, 471 p. 32 illus., 14 illus. in color. - ISBN 9783319528427
    Зміст:

Рубрики: Differential equations.
   Partial differential equations.
   Differential geometry.
   Mathematical physics.
   Number theory.
   Ordinary Differential Equations.
   Partial Differential Equations.
   Differential Geometry.
   Mathematical Physics.
   Number Theory.
Анотація: This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Będlewo, Poland in September 2015. The contributions provide an overview of the current level of interaction between algebra, geometry and analysis and demonstrate the manifold aspects of the theory of ordinary and partial differential equations, while also pointing out the highly fruitful interrelations between those aspects. These interactions continue to yield new developments, not only in the theory of differential equations but also in several related areas of mathematics and physics such as differential geometry, representation theory, number theory and mathematical physics. The main goal of the volume is to introduce basic concepts, techniques, detailed and illustrative examples and theorems (in a manner suitable for non-specialists), and to present recent developments in the field, together with open problems for more advanced and experienced readers. It will be of interest to graduate students, early-career researchers and specialists in analysis, geometry, algebra and related areas, as well as anyone interested in learning new methods and techniques.
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Filipuk, Galina. \ed.\; Haraoka, Yoshishige. \ed.\; Michalik, Sławomir. \ed.\
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17.

    Rudolph, Gerd.
    Differential Geometry and Mathematical Physics [Electronic resource] : part II. Fibre Bundles, Topology and Gauge Fields / / Gerd. Rudolph, Schmidt, Matthias. ; . - 1st ed. 2017. - [S. l. : s. n.]. - XVI, 830 p. 15 illus., 2 illus. in color. - ISBN 9789402409598
    Зміст:

Рубрики: Physics.
   Differential geometry.
   Mathematical physics.
   Algebraic geometry.
   Algebraic topology.
   Elementary particles (Physics).
   Quantum field theory.
   Mathematical Methods in Physics.
   Differential Geometry.
   Mathematical Physics.
   Algebraic Geometry.
   Algebraic Topology.
   Elementary Particles, Quantum Field Theory.
Анотація: The book is devoted to the study of the geometrical and topological structure of gauge theories. It consists of the following three building blocks: - Geometry and topology of fibre bundles, - Clifford algebras, spin structures and Dirac operators, - Gauge theory. Written in the style of a mathematical textbook, it combines a comprehensive presentation of the mathematical foundations with a discussion of a variety of advanced topics in gauge theory. The first building block includes a number of specific topics, like invariant connections, universal connections, H-structures and the Postnikov approximation of classifying spaces. Given the great importance of Dirac operators in gauge theory, a complete proof of the Atiyah-Singer Index Theorem is presented. The gauge theory part contains the study of Yang-Mills equations (including the theory of instantons and the classical stability analysis), the discussion of various models with matter fields (including magnetic monopoles, the Seiberg-Witten model and dimensional reduction) and the investigation of the structure of the gauge orbit space. The final chapter is devoted to elements of quantum gauge theory including the discussion of the Gribov problem, anomalies and the implementation of the non-generic gauge orbit strata in the framework of Hamiltonian lattice gauge theory. The book is addressed both to physicists and mathematicians. It is intended to be accessible to students starting from a graduate level.
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Schmidt, Matthias.; Rudolph, Gerd. \.\
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18.

    Hollings, Christopher D.
    Wagner’s Theory of Generalised Heaps [Electronic resource] / Christopher D. Hollings, Lawson, Mark V. ; . - 1st ed. 2017. - [S. l. : s. n.]. - XV, 189 p. 19 illus. - ISBN 9783319636214
    Зміст:

Рубрики: Group theory.
   Mathematics.
   History.
   Differential geometry.
   Group Theory and Generalizations.
   History of Mathematical Sciences.
   Differential Geometry.
Анотація: The theories of V. V. Wagner (1908-1981) on abstractions of systems of binary relations are presented here within their historical and mathematical contexts. This book contains the first translation from Russian into English of a selection of Wagner’s papers, the ideas of which are connected to present-day mathematical research. Along with a translation of Wagner’s main work in this area, his 1953 paper ‘Theory of generalised heaps and generalised groups,’ the book also includes translations of three short precursor articles that provide additional context for his major work. Researchers and students interested in both algebra (in particular, heaps, semiheaps, generalised heaps, semigroups, and groups) and differential geometry will benefit from the techniques offered by these translations, owing to the natural connections between generalised heaps and generalised groups, and the role played by these concepts in differential geometry. This book gives examples from present-day mathematics where ideas related to Wagner’s have found fruitful applications.
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Lawson, Mark V.; Hollings, Christopher D. \.\
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19.

    From Riemann to Differential Geometry and Relativity [Electronic resource] / ed.: Ji, Lizhen., Papadopoulos, Athanase., Yamada, Sumio. - 1st ed. 2017. - [S. l. : s. n.]. - XXXIV, 647 p. 24 illus. - ISBN 9783319600390
    Зміст:

Рубрики: Mathematics.
   History.
   Differential geometry.
   History of Mathematical Sciences.
   Differential Geometry.
Анотація: This book explores the work of Bernhard Riemann and its impact on mathematics, philosophy and physics. It features contributions from a range of fields, historical expositions, and selected research articles that were motivated by Riemann’s ideas and demonstrate their timelessness. The editors are convinced of the tremendous value of going into Riemann’s work in depth, investigating his original ideas, integrating them into a broader perspective, and establishing ties with modern science and philosophy. Accordingly, the contributors to this volume are mathematicians, physicists, philosophers and historians of science. The book offers a unique resource for students and researchers in the fields of mathematics, physics and philosophy, historians of science, and more generally to a wide range of readers interested in the history of ideas.
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Ji, Lizhen. \ed.\; Papadopoulos, Athanase. \ed.\; Yamada, Sumio. \ed.\
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20.

    Kodaira, Kunihiko.
    Nevanlinna Theory [Electronic resource] / Kunihiko. Kodaira ; . - 1st ed. 2017. - [S. l. : s. n.]. - XI, 86 p. 30 illus. - ISBN 9789811067877
Рубрики: Functions of complex variables.
   Algebraic geometry.
   Differential geometry.
   Several Complex Variables and Analytic Spaces.
   Algebraic Geometry.
   Differential Geometry.
Анотація: This book deals with the classical theory of Nevanlinna on the value distribution of meromorphic functions of one complex variable, based on minimum prerequisites for complex manifolds. The theory was extended to several variables by S. Kobayashi, T. Ochiai, J. Carleson, and P. Griffiths in the early 1970s. K. Kodaira took up this subject in his course at The University of Tokyo in 1973 and gave an introductory account of this development in the context of his final paper, contained in this book. The first three chapters are devoted to holomorphic mappings from C to complex manifolds. In the fourth chapter, holomorphic mappings between higher dimensional manifolds are covered. The book is a valuable treatise on the Nevanlinna theory, of special interests to those who want to understand Kodaira's unique approach to basic questions on complex manifolds.
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