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Diffeology

Diffeology Author Patrick Iglesias-Zemmour
ISBN-10 9780821891315
Release 2013-04-09
Pages 439
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Diffeology is an extension of differential geometry. With a minimal set of axioms, diffeology allows us to deal simply but rigorously with objects which do not fall within the usual field of differential geometry: quotients of manifolds (even non-Hausdorff), spaces of functions, groups of diffeomorphisms, etc. The category of diffeology objects is stable under standard set-theoretic operations, such as quotients, products, co-products, subsets, limits, and co-limits. With its right balance between rigor and simplicity, diffeology can be a good framework for many problems that appear in various areas of physics. Actually, the book lays the foundations of the main fields of differential geometry used in theoretical physics: differentiability, Cartan differential calculus, homology and cohomology, diffeological groups, fiber bundles, and connections. The book ends with an open program on symplectic diffeology, a rich field of application of the theory. Many exercises with solutions make this book appropriate for learning the subject.



Diffeology

Diffeology Author Patrick Iglesias-Zemmour
ISBN-10 9780821891315
Release 2013-04-09
Pages 439
Download Link Click Here

Diffeology is an extension of differential geometry. With a minimal set of axioms, diffeology allows us to deal simply but rigorously with objects which do not fall within the usual field of differential geometry: quotients of manifolds (even non-Hausdorff), spaces of functions, groups of diffeomorphisms, etc. The category of diffeology objects is stable under standard set-theoretic operations, such as quotients, products, co-products, subsets, limits, and co-limits. With its right balance between rigor and simplicity, diffeology can be a good framework for many problems that appear in various areas of physics. Actually, the book lays the foundations of the main fields of differential geometry used in theoretical physics: differentiability, Cartan differential calculus, homology and cohomology, diffeological groups, fiber bundles, and connections. The book ends with an open program on symplectic diffeology, a rich field of application of the theory. Many exercises with solutions make this book appropriate for learning the subject.



Mathematics Across Contemporary Sciences

Mathematics Across Contemporary Sciences Author Taher Abualrub
ISBN-10 9783319463100
Release 2017-02-24
Pages 259
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This work presents invited contributions from the second "International Conference on Mathematics and Statistics" jointly organized by the AUS (American University of Sharjah) and the AMS (American Mathematical Society). Addressing several research fields across the mathematical sciences, all of the papers were prepared by faculty members at universities in the Gulf region or prominent international researchers. The current volume is the first of its kind in the UAE and is intended to set new standards of excellence for collaboration and scholarship in the region.



Mathematics Without Boundaries

Mathematics Without Boundaries Author Themistocles Rassias
ISBN-10 9781493911066
Release 2014-09-17
Pages 781
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The contributions in this volume have been written by eminent scientists from the international mathematical community and present significant advances in several theories, methods and problems of Mathematical Analysis, Discrete Mathematics, Geometry and their Applications. The chapters focus on both old and recent developments in Functional Analysis, Harmonic Analysis, Complex Analysis, Operator Theory, Combinatorics, Functional Equations, Differential Equations as well as a variety of Applications. The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical Sciences, and especially to graduate students looking for the latest information.



Algebra Geometry and Physics in the 21st Century

Algebra  Geometry  and Physics in the 21st Century Author Denis Auroux
ISBN-10 9783319599397
Release 2017-08-16
Pages 358
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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



Towards the Mathematics of Quantum Field Theory

Towards the Mathematics of Quantum Field Theory Author Frederic Paugam
ISBN-10 9783319045641
Release 2014-02-20
Pages 487
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This ambitious and original book sets out to introduce to mathematicians (even including graduate students ) the mathematical methods of theoretical and experimental quantum field theory, with an emphasis on coordinate-free presentations of the mathematical objects in use. This in turn promotes the interaction between mathematicians and physicists by supplying a common and flexible language for the good of both communities, though mathematicians are the primary target. This reference work provides a coherent and complete mathematical toolbox for classical and quantum field theory, based on categorical and homotopical methods, representing an original contribution to the literature. The first part of the book introduces the mathematical methods needed to work with the physicists' spaces of fields, including parameterized and functional differential geometry, functorial analysis, and the homotopical geometric theory of non-linear partial differential equations, with applications to general gauge theories. The second part presents a large family of examples of classical field theories, both from experimental and theoretical physics, while the third part provides an introduction to quantum field theory, presents various renormalization methods, and discusses the quantization of factorization algebras.



The Convenient Setting of Global Analysis

The Convenient Setting of Global Analysis Author Andreas Kriegl
ISBN-10 9780821807804
Release 1997
Pages 618
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This book lays the foundations of differential calculus in infinite dimensions and discusses those applications in infinite dimensional differential geometry and global analysis not involving Sobolev completions and fixed point theory. The approach is simple: a mapping is called smooth if it maps smooth curves to smooth curves. Up to Frechet spaces, this notion of smoothness coincides with all known reasonable concepts. In the same spirit, calculus of holomorphic mappings (including Hartogs' theorem and holomorphic uniform boundedness theorems) and calculus of real analytic mappings are developed. Existence of smooth partitions of unity, the foundations of manifold theory in infinite dimensions, the relation between tangent vectors and derivations, and differential forms are discussed thoroughly. Special emphasis is given to the notion of regular infinite dimensional Lie groups. Many applications of this theory are included: manifolds of smooth mappings, groups of diffeomorphisms, geodesics on spaces of Riemannian metrics, direct limit manifolds, perturbation theory of operators, and differentiability questions of infinite dimensional representations.



Persistence Theory From Quiver Representations to Data Analysis

Persistence Theory  From Quiver Representations to Data Analysis Author Steve Y. Oudot
ISBN-10 9781470434434
Release 2017-05-17
Pages 218
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Persistence theory emerged in the early 2000s as a new theory in the area of applied and computational topology. This book provides a broad and modern view of the subject, including its algebraic, topological, and algorithmic aspects. It also elaborates on applications in data analysis. The level of detail of the exposition has been set so as to keep a survey style, while providing sufficient insights into the proofs so the reader can understand the mechanisms at work. The book is organized into three parts. The first part is dedicated to the foundations of persistence and emphasizes its connection to quiver representation theory. The second part focuses on its connection to applications through a few selected topics. The third part provides perspectives for both the theory and its applications. The book can be used as a text for a course on applied topology or data analysis.



Quantum Field Theory

Quantum Field Theory Author G. B. Folland
ISBN-10 9780821847053
Release 2008-08-26
Pages 325
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Quantum field theory has been a great success for physics, but it is difficult for mathematicians to learn because it is mathematically incomplete. Folland, who is a mathematician, has spent considerable time digesting the physical theory and sorting out the mathematical issues in it. Fortunately for mathematicians, Folland is a gifted expositor. The purpose of this book is to present the elements of quantum field theory, with the goal of understanding the behavior of elementary particles rather than building formal mathematical structures, in a form that will be comprehensible to mathematicians. Rigorous definitions and arguments are presented as far as they are available, but the text proceeds on a more informal level when necessary, with due care in identifying the difficulties. The book begins with a review of classical physics and quantum mechanics, then proceeds through the construction of free quantum fields to the perturbation-theoretic development of interacting field theory and renormalization theory, with emphasis on quantum electrodynamics. The final two chapters present the functional integral approach and the elements of gauge field theory, including the Salam-Weinberg model of electromagnetic and weak interactions.



Grid Homology for Knots and Links

Grid Homology for Knots and Links Author Peter S. Ozsváth
ISBN-10 9781470417376
Release 2015-12-04
Pages 410
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Knot theory is a classical area of low-dimensional topology, directly connected with the theory of three-manifolds and smooth four-manifold topology. In recent years, the subject has undergone transformative changes thanks to its connections with a number of other mathematical disciplines, including gauge theory; representation theory and categorification; contact geometry; and the theory of pseudo-holomorphic curves. Starting from the combinatorial point of view on knots using their grid diagrams, this book serves as an introduction to knot theory, specifically as it relates to some of the above developments. After a brief overview of the background material in the subject, the book gives a self-contained treatment of knot Floer homology from the point of view of grid diagrams. Applications include computations of the unknotting number and slice genus of torus knots (asked first in the 1960s and settled in the 1990s), and tools to study variants of knot theory in the presence of a contact structure. Additional topics are presented to prepare readers for further study in holomorphic methods in low-dimensional topology, especially Heegaard Floer homology. The book could serve as a textbook for an advanced undergraduate or part of a graduate course in knot theory. Standard background material is sketched in the text and the appendices.



The Water Waves Problem

The Water Waves Problem Author David Lannes
ISBN-10 9780821894705
Release 2013-05-08
Pages 321
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This monograph provides a comprehensive and self-contained study on the theory of water waves equations, a research area that has been very active in recent years. The vast literature devoted to the study of water waves offers numerous asymptotic models.



Birationally Rigid Varieties

Birationally Rigid Varieties Author Aleksandr V. Pukhlikov
ISBN-10 9780821894767
Release 2013-05-15
Pages 367
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Birational rigidity is a striking and mysterious phenomenon in higher-dimensional algebraic geometry. It turns out that certain natural families of algebraic varieties (for example, three-dimensional quartics) belong to the same classification type as the



Comptes Rendus Math matiques de L Acad mie Des Sciences

Comptes Rendus Math  matiques de L Acad  mie Des Sciences Author
ISBN-10 UOM:39015072612099
Release 2005
Pages
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Comptes Rendus Math matiques de L Acad mie Des Sciences has been writing in one form or another for most of life. You can find so many inspiration from Comptes Rendus Math matiques de L Acad mie Des Sciences also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Comptes Rendus Math matiques de L Acad mie Des Sciences book for free.



The Moment Maps in Diffeology

The Moment Maps in Diffeology Author Patrick Iglesias-Zemmour
ISBN-10 9780821847091
Release 2010
Pages 72
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This memoir presents a generalization of the moment maps to the category $\{$Diffeology$\}$. This construction applies to every smooth action of any diffeological group $\mathrm{G}$ preserving a closed 2-form $\omega$, defined on some diffeological space $\mathrm{X}$. In particular, that reveals a universal construction, associated to the action of the whole group of automorphisms $\mathrm{Diff}(\mathrm{X},\omega)$. By considering directly the space of momenta of any diffeological group $\mathrm{G}$, that is the space $\mathscr{G}^*$ of left-invariant 1-forms on $\mathrm{G}$, this construction avoids any reference to Lie algebra or any notion of vector fields, or does not involve any functional analysis. These constructions of the various moment maps are illustrated by many examples, some of them originals and others suggested by the mathematical literature.



Factorization Algebras in Quantum Field Theory

Factorization Algebras in Quantum Field Theory Author Kevin Costello
ISBN-10 9781107163102
Release 2016-12-15
Pages 398
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This first volume develops factorization algebras with a focus upon examples exhibiting their use in field theory, which will be useful for researchers and graduates.



Algebraic Geometric Codes

Algebraic Geometric Codes Author M. Tsfasman
ISBN-10 9789401138109
Release 2013-12-01
Pages 667
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Algebraic Geometric Codes has been writing in one form or another for most of life. You can find so many inspiration from Algebraic Geometric Codes also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Algebraic Geometric Codes book for free.



Quaestiones Mathematicae

Quaestiones Mathematicae Author
ISBN-10 UOM:39015059001142
Release 2005
Pages
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Quaestiones Mathematicae has been writing in one form or another for most of life. You can find so many inspiration from Quaestiones Mathematicae also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Quaestiones Mathematicae book for free.