Topological Field Theory Primitive Forms And Related Topics
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Topological Field Theory Primitive Forms And Related Topics
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Author : A. Kashiwara
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Topological Field Theory Primitive Forms And Related Topics written by A. Kashiwara 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 2012-12-06 with Mathematics categories.
As the interaction of mathematics and theoretical physics continues to intensify, the theories developed in mathematics are being applied to physics, and conversely. This book centers around the theory of primitive forms which currently plays an active and key role in topological field theory (theoretical physics), but was originally developed as a mathematical notion to define a "good period mapping" for a family of analytic structures. The invited papers in this volume are expository in nature by participants of the Taniguchi Symposium on "Topological Field Theory, Primitive Forms and Related Topics" and the RIMS Symposium bearing the same title, both held in Kyoto. The papers reflect the broad research of some of the world's leading mathematical physicists, and should serve as an excellent resource for researchers as well as graduate students of both disciplines.
Topological Field Theory Primitive Forms And Related Topics
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Author : Masaki Kashiwara
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-12
Topological Field Theory Primitive Forms And Related Topics written by Masaki Kashiwara 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 1998-12 with Mathematics categories.
As the interaction of mathematics and theoretical physics continues to intensify, the theories developed in mathematics are being applied to physics, and conversely. This book centers around the theory of primitive forms which currently plays an active and key role in topological field theory (theoretical physics), but was originally developed as a mathematical notion to define a "good period mapping" for a family of analytic structures. The invited papers in this volume are expository in nature by participants of the Taniguchi Symposium on "Topological Field Theory, Primitive Forms and Related Topics" and the RIMS Symposium bearing the same title, both held in Kyoto. The papers reflect the broad research of some of the world's leading mathematical physicists, and should serve as an excellent resource for researchers as well as graduate students of both disciplines.
Topological Field Theory Primitive Forms And Related Topics
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Author : A. Kashiwara
language : en
Publisher:
Release Date : 1998-12-01
Topological Field Theory Primitive Forms And Related Topics written by A. Kashiwara and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-12-01 with categories.
Lie Theory
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Author : Jean-Philippe Anker
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lie Theory written by Jean-Philippe Anker 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 2012-12-06 with Mathematics categories.
Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics. Three independent, self-contained volumes, under the general title "Lie Theory," feature survey work and original results by well-established researchers in key areas of semisimple Lie theory. A wide spectrum of topics is treated, with emphasis on the interplay between representation theory and the geometry of adjoint orbits for Lie algebras over fields of possibly finite characteristic, as well as for infinite-dimensional Lie algebras. Also covered is unitary representation theory and branching laws for reductive subgroups, an active part of modern representation theory. Finally, there is a thorough discussion of compactifications of symmetric spaces, and harmonic analysis through a far-reaching generalization of Harish--Chandra's Plancherel formula for semisimple Lie groups. Ideal for graduate students and researchers, "Lie Theory" provides a broad, clearly focused examination of semisimple Lie groups and their integral importance to research in many branches of mathematics.
Mirror Symmetry
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Author : Kentaro Hori
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Mirror Symmetry written by Kentaro Hori 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 2003 with Mathematics categories.
This thorough and detailed exposition is the result of an intensive month-long course on mirror symmetry sponsored by the Clay Mathematics Institute. It develops mirror symmetry from both mathematical and physical perspectives with the aim of furthering interaction between the two fields. The material will be particularly useful for mathematicians and physicists who wish to advance their understanding across both disciplines. Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics. Such a correspondence has significant mathematical consequences, the most familiar of which involves the enumeration of holomorphic curves inside complex manifolds by solving differential equations obtained from a ``mirror'' geometry. The inclusion of D-brane states in the equivalence has led to further conjectures involving calibrated submanifolds of the mirror pairs and new (conjectural) invariants of complex manifolds: the Gopakumar-Vafa invariants. This book gives a single, cohesive treatment of mirror symmetry. Parts 1 and 2 develop the necessary mathematical and physical background from ``scratch''. The treatment is focused, developing only the material most necessary for the task. In Parts 3 and 4 the physical and mathematical proofs of mirror symmetry are given. From the physics side, this means demonstrating that two different physical theories give isomorphic physics. Each physical theory can be described geometrically, and thus mirror symmetry gives rise to a ``pairing'' of geometries. The proof involves applying $R\leftrightarrow 1/R$ circle duality to the phases of the fields in the gauged linear sigma model. The mathematics proof develops Gromov-Witten theory in the algebraic setting, beginning with the moduli spaces of curves and maps, and uses localization techniques to show that certain hypergeometric functions encode the Gromov-Witten invariants in genus zero, as is predicted by mirror symmetry. Part 5 is devoted to advanced topi This one-of-a-kind book is suitable for graduate students and research mathematicians interested in mathematics and mathematical and theoretical physics.
D Modules Perverse Sheaves And Representation Theory
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Author : Ryoshi Hotta
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-07
D Modules Perverse Sheaves And Representation Theory written by Ryoshi Hotta 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 2007-11-07 with Mathematics categories.
D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors' essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, representation theory.
The Painlev Property
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Author : Robert Conte
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Painlev Property written by Robert Conte 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 2012-12-06 with Science categories.
The subject this volume is explicit integration, that is, the analytical as opposed to the numerical solution, of all kinds of nonlinear differential equations (ordinary differential, partial differential, finite difference). Such equations describe many physical phenomena, their analytic solutions (particular solutions, first integral, and so forth) are in many cases preferable to numerical computation, which may be long, costly and, worst, subject to numerical errors. In addition, the analytic approach can provide a global knowledge of the solution, while the numerical approach is always local. Explicit integration is based on the powerful methods based on an in-depth study of singularities, that were first used by Poincar and subsequently developed by Painlev in his famous Leons de Stockholm of 1895. The recent interest in the subject and in the equations investigated by Painlev dates back about thirty years ago, arising from three, apparently disjoint, fields: the Ising model of statistical physics and field theory, propagation of solitons, and dynamical systems. The chapters in this volume, based on courses given at Cargse 1998, alternate mathematics and physics; they are intended to bring researchers entering the field to the level of present research.
Frobenius Manifolds
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Author : Claus Hertling
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Frobenius Manifolds written by Claus Hertling 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 2012-12-06 with Mathematics categories.
Quantum cohomology, the theory of Frobenius manifolds and the relations to integrable systems are flourishing areas since the early 90's. An activity was organized at the Max-Planck-Institute for Mathematics in Bonn, with the purpose of bringing together the main experts in these areas. This volume originates from this activity and presents the state of the art in the subject.
B Model Gromov Witten Theory
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Author : Emily Clader
language : en
Publisher: Springer
Release Date : 2019-04-08
B Model Gromov Witten Theory written by Emily Clader and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-08 with Mathematics categories.
This book collects various perspectives, contributed by both mathematicians and physicists, on the B-model and its role in mirror symmetry. Mirror symmetry is an active topic of research in both the mathematics and physics communities, but among mathematicians, the “A-model” half of the story remains much better-understood than the B-model. This book aims to address that imbalance. It begins with an overview of several methods by which mirrors have been constructed, and from there, gives a thorough account of the “BCOV” B-model theory from a physical perspective; this includes the appearance of such phenomena as the holomorphic anomaly equation and connections to number theory via modularity. Following a mathematical exposition of the subject of quantization, the remainder of the book is devoted to the B-model from a mathematician’s point-of-view, including such topics as polyvector fields and primitive forms, Givental’s ancestor potential, and integrablesystems.
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.