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Orbifolds In Mathematics And Physics


Orbifolds In Mathematics And Physics
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Orbifolds In Mathematics And Physics


Orbifolds In Mathematics And Physics
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Author : Alejandro Adem
language : en
Publisher: American Mathematical Soc.
Release Date : 2002

Orbifolds In Mathematics And Physics written by Alejandro Adem and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.


This book publishes papers originally presented at a conference on the Mathematical Aspects of Orbifold String Theory, hosted by the University of Wisconsin-Madison. It contains a great deal of information not fully covered in the published literature and showcases the current state of the art in orbital string theory. The subject of orbifolds has a long prehistory, going back to the work of Thurston and Haefliger, with roots in the theory of manifolds, group actions, and foliations. The recent explosion of activity on the topic has been powered by applications of orbifolds to moduli problems and quantum field theory. The present volume presents an interdisciplinary look at orbifold problems. Topics such as stacks, vertex operator algebras, branes, groupoids, K-theory and quantum cohomology are discussed. The book reflects the thinking of distinguished investigators working in the areas of mathematical physics, algebraic geometry, algebraic topology, symplectic geometry and representation theory. By presenting the work of a broad range of mathematicians and physicists who use and study orbifolds, it familiarizes readers with the various points of view and types of results the researchers bring to the subject.



Geometric And Topological Methods For Quantum Field Theory


Geometric And Topological Methods For Quantum Field Theory
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Author : Hernan Ocampo
language : en
Publisher: Cambridge University Press
Release Date : 2010-04-29

Geometric And Topological Methods For Quantum Field Theory written by Hernan Ocampo and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-29 with Science categories.


Aimed at graduate students in physics and mathematics, this book provides an introduction to recent developments in several active topics at the interface between algebra, geometry, topology and quantum field theory. The first part of the book begins with an account of important results in geometric topology. It investigates the differential equation aspects of quantum cohomology, before moving on to noncommutative geometry. This is followed by a further exploration of quantum field theory and gauge theory, describing AdS/CFT correspondence, and the functional renormalization group approach to quantum gravity. The second part covers a wide spectrum of topics on the borderline of mathematics and physics, ranging from orbifolds to quantum indistinguishability and involving a manifold of mathematical tools borrowed from geometry, algebra and analysis. Each chapter presents introductory material before moving on to more advanced results. The chapters are self-contained and can be read independently of the rest.



Quarks And Leptons From Orbifolded Superstring


Quarks And Leptons From Orbifolded Superstring
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Author : Kang-Sin Choi
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-23

Quarks And Leptons From Orbifolded Superstring written by Kang-Sin Choi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-23 with Science categories.


This book offers a detailed guide on the journey towards the minimal supersymmetric standard model down the orbifold road. It takes the viewpoint that the chirality of matter fermions is an essential aspect that orbifold compactification allows to derive from higher-dimensional string theories in a straightforward manner. Halfway between textbook and tutorial review, the book is intended for the graduate student and particle phenomenologist wishing to get acquainted with this field.



Three Dimensional Orbifolds And Their Geometric Structures


Three Dimensional Orbifolds And Their Geometric Structures
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Author : Michel Boileau
language : en
Publisher:
Release Date : 2003

Three Dimensional Orbifolds And Their Geometric Structures written by Michel Boileau and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.


Orbifolds locally look like quotients of manifolds by finite group actions. They play an important role in the study of proper actions of discrete groups on manifolds. This monograph presents recent fundamental results on the geometry and topology of 3-dimensional orbifolds, with an emphasis on their geometric properties. It is suitable for graduate students and research mathematicians interested in geometry and topology.



Orbifolds And Stringy Topology


Orbifolds And Stringy Topology
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Author : Alejandro Adem
language : en
Publisher: Cambridge University Press
Release Date : 2007-05-31

Orbifolds And Stringy Topology written by Alejandro Adem and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-31 with Mathematics categories.


An introduction to the theory of orbifolds from a modern perspective, combining techniques from geometry, algebraic topology and algebraic geometry. One of the main motivations, and a major source of examples, is string theory, where orbifolds play an important role. The subject is first developed following the classical description analogous to manifold theory, after which the book branches out to include the useful description of orbifolds provided by groupoids, as well as many examples in the context of algebraic geometry. Classical invariants such as de Rham cohomology and bundle theory are developed, a careful study of orbifold morphisms is provided, and the topic of orbifold K-theory is covered. The heart of this book, however, is a detailed description of the Chen-Ruan cohomology, which introduces a product for orbifolds and has had significant impact. The final chapter includes explicit computations for a number of interesting examples.



The Geometry And Physics Of Knots


The Geometry And Physics Of Knots
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Author : Michael Francis Atiyah
language : en
Publisher: Cambridge University Press
Release Date : 1990-08-23

The Geometry And Physics Of Knots written by Michael Francis Atiyah and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-08-23 with Mathematics categories.


These notes deal with an area that lies at the crossroads of mathematics and physics and rest primarily on the pioneering work of Vaughan Jones and Edward Witten, who related polynomial invariants of knots to a topological quantum field theory in 2+1 dimensions.



Spectral Geometry


Spectral Geometry
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Author : Alex Barnett
language : en
Publisher: American Mathematical Soc.
Release Date : 2012

Spectral Geometry written by Alex Barnett and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.


This volume contains the proceedings of the International Conference on Spectral Geometry, held July 19-23, 2010, at Dartmouth College, Dartmouth, New Hampshire. Eigenvalue problems involving the Laplace operator on manifolds have proven to be a consistently fertile area of geometric analysis with deep connections to number theory, physics, and applied mathematics. Key questions include the measures to which eigenfunctions of the Laplacian on a Riemannian manifold condense in the limit of large eigenvalue, and the extent to which the eigenvalues and eigenfunctions of a manifold encode its geometry. In this volume, research and expository articles, including those of the plenary speakers Peter Sarnak and Victor Guillemin, address the flurry of recent progress in such areas as quantum unique ergodicity, isospectrality, semiclassical measures, the geometry of nodal lines of eigenfunctions, methods of numerical computation, and spectra of quantum graphs. This volume also contains mini-courses on spectral theory for hyperbolic surfaces, semiclassical analysis, and orbifold spectral geometry that prepared the participants, especially graduate students and young researchers, for conference lectures.



On Representations Of Conformal Field Theories And The Construction Of Orbifolds


On Representations Of Conformal Field Theories And The Construction Of Orbifolds
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Author : P. S. Montague
language : en
Publisher:
Release Date : 1995

On Representations Of Conformal Field Theories And The Construction Of Orbifolds written by P. S. Montague and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Physics categories.




Gromov Witten Theory Of Spin Curves And Orbifolds


Gromov Witten Theory Of Spin Curves And Orbifolds
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Author : Tyler Jamison Jarvis
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

Gromov Witten Theory Of Spin Curves And Orbifolds written by Tyler Jamison Jarvis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.


This volume is a collection of articles on orbifolds, algebraic curves with higher spin structures, and related invariants of Gromov-Witten type. Orbifold Gromov-Witten theory generalizes quantum cohomology for orbifolds, whereas spin cohomological field theory is based on the moduli spaces of higher spin curves and is related by Witten's conjecture to the Gelfand-Dickey integrable hierarchies. A common feature of these two very different looking theories is the central role played by orbicurves in both of them. Insights in one theory can often yield insights into the other. This book brings together for the first time papers related to both sides of this interaction. The articles in the collection cover diverse topics, such as geometry and topology of orbifolds, cohomological field theories, orbifold Gromov-Witten theory, $G$-Frobenius algebra and singularities, Frobenius manifolds and Givental's quantization formalism, moduli of higher spin curves and spin cohomological field theory.



Vertex Operator Algebras In Mathematics And Physics


Vertex Operator Algebras In Mathematics And Physics
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Author : Stephen Berman
language : en
Publisher: American Mathematical Soc.
Release Date :

Vertex Operator Algebras In Mathematics And Physics written by Stephen Berman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.


Vertex operator algebras are a class of algebras underlying a number of recent constructions, results, and themes in mathematics. These algebras can be understood as ''string-theoretic analogues'' of Lie algebras and of commutative associative algebras. They play fundamental roles in some of the most active research areas in mathematics and physics. Much recent progress in both physics and mathematics has benefited from cross-pollination between the physical and mathematical points of view. This book presents the proceedings from the workshop, ''Vertex Operator Algebras in Mathematics and Physics'', held at The Fields Institute. It consists of papers based on many of the talks given at the conference by leading experts in the algebraic, geometric, and physical aspects of vertex operator algebra theory. The book is suitable for graduate students and research mathematicians interested in the major themes and important developments on the frontier of research in vertex operator algebra theory and its applications in mathematics and physics.