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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.



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.



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



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.



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.



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.



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.