Frobenius Manifolds Quantum Cohomology And Moduli Spaces

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Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces

Author : I︠U︡. I. Manin
Publisher : American Mathematical Soc.
ISBN 13 : 0821819178
Total Pages : 321 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces by : I︠U︡. I. Manin

Download or read book Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces written by I︠U︡. I. Manin and published by American Mathematical Soc.. This book was released on 1999 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first monograph dedicated to the systematic exposition of the whole variety of topics related to quantum cohomology. The subject first originated in theoretical physics (quantum string theory) and has continued to develop extensively over the last decade. The author's approach to quantum cohomology is based on the notion of the Frobenius manifold. The first part of the book is devoted to this notion and its extensive interconnections with algebraic formalism of operads, differential equations, perturbations, and geometry. In the second part of the book, the author describes the construction of quantum cohomology and reviews the algebraic geometry mechanisms involved in this construction (intersection and deformation theory of Deligne-Artin and Mumford stacks). Yuri Manin is currently the director of the Max-Planck-Institut für Mathematik in Bonn, Germany. He has authored and coauthored 10 monographs and almost 200 research articles in algebraic geometry, number theory, mathematical physics, history of culture, and psycholinguistics. Manin's books, such as Cubic Forms: Algebra, Geometry, and Arithmetic (1974), A Course in Mathematical Logic (1977), Gauge Field Theory and Complex Geometry (1988), Elementary Particles: Mathematics, Physics and Philosophy (1989, with I. Yu. Kobzarev), Topics in Non-commutative Geometry (1991), and Methods of Homological Algebra (1996, with S. I. Gelfand), secured for him solid recognition as an excellent expositor. Undoubtedly the present book will serve mathematicians for many years to come.

Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces

Author : I︠U︡. I. Manin
Publisher :
ISBN 13 : 9781470431938
Total Pages : pages
Book Rating : 4.4/5 (319 download)

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Book Synopsis Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces by : I︠U︡. I. Manin

Download or read book Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces written by I︠U︡. I. Manin and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first monograph dedicated to the systematic exposition of the whole variety of topics related to quantum cohomology. The subject first originated in theoretical physics (quantum string theory) and has continued to develop extensively over the last decade. The author's approach to quantum cohomology is based on the notion of the Frobenius manifold. The first part of the book is devoted to this notion and its extensive interconnections with algebraic formalism of operads, differential equations, perturbations, and geometry. In the second part of the book, the author describes the con.

Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces

Author : I͡U. I. Manin
Publisher : American Mathematical Soc.
ISBN 13 : 9780821874752
Total Pages : 330 pages
Book Rating : 4.8/5 (747 download)

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Book Synopsis Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces by : I͡U. I. Manin

Download or read book Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces written by I͡U. I. Manin and published by American Mathematical Soc.. This book was released on with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Frobenius Manifolds

Author : Claus Hertling
Publisher : Springer Science & Business Media
ISBN 13 : 3322802361
Total Pages : 384 pages
Book Rating : 4.3/5 (228 download)

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Book Synopsis Frobenius Manifolds by : Claus Hertling

Download or read book Frobenius Manifolds written by Claus Hertling and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Frobenius Manifolds and Moduli Spaces for Singularities

Author : Claus Hertling
Publisher : Cambridge University Press
ISBN 13 : 9780521812962
Total Pages : 292 pages
Book Rating : 4.8/5 (129 download)

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Book Synopsis Frobenius Manifolds and Moduli Spaces for Singularities by : Claus Hertling

Download or read book Frobenius Manifolds and Moduli Spaces for Singularities written by Claus Hertling and published by Cambridge University Press. This book was released on 2002-07-25 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the theory of Frobenius manifolds, as well as all the necessary tools and several applications.

The Geometry of Moduli Spaces of Pointed Curves, the Tensor Product in the Theory of Frobenius Manifolds and the Explicit Künneth Formula in Quantum Cohomology

Download The Geometry of Moduli Spaces of Pointed Curves, the Tensor Product in the Theory of Frobenius Manifolds and the Explicit Künneth Formula in Quantum Cohomology PDF Online Free

Author : Ralph M. Kaufmann
Publisher :
ISBN 13 :
Total Pages : 106 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis The Geometry of Moduli Spaces of Pointed Curves, the Tensor Product in the Theory of Frobenius Manifolds and the Explicit Künneth Formula in Quantum Cohomology by : Ralph M. Kaufmann

Download or read book The Geometry of Moduli Spaces of Pointed Curves, the Tensor Product in the Theory of Frobenius Manifolds and the Explicit Künneth Formula in Quantum Cohomology written by Ralph M. Kaufmann and published by . This book was released on 1998 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt:

J-holomorphic Curves and Quantum Cohomology

Author : Dusa McDuff
Publisher : American Mathematical Soc.
ISBN 13 : 0821803328
Total Pages : 207 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis J-holomorphic Curves and Quantum Cohomology by : Dusa McDuff

Download or read book J-holomorphic Curves and Quantum Cohomology written by Dusa McDuff and published by American Mathematical Soc.. This book was released on 1994 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: $J$-holomorphic curves revolutionized the study of symplectic geometry when Gromov first introduced them in 1985. Through quantum cohomology, these curves are now linked to many of the most exciting new ideas in mathematical physics. This book presents the first coherent and full account of the theory of $J$-holomorphic curves, the details of which are presently scattered in various research papers. The first half of the book is an expository account of the field, explaining the main technical aspects. McDuff and Salamon give complete proofs of Gromov's compactness theorem for spheres and of the existence of the Gromov-Witten invariants. The second half of the book focuses on the definition of quantum cohomology. The authors establish that this multiplication exists, and give a new proof of the Ruan-Tian result that is associative on appropriate manifolds. They then describe the Givental-Kim calculation of the quantum cohomology of flag manifolds, leading to quantum Chern classes and Witten's calculation for Grassmannians, which relates to the Verlinde algebra. The Dubrovin connection, Gromov-Witten potential on quantum cohomology, and curve counting formulas are also discussed. The book closes with an outline of connections to Floer theory.

An Invitation to Quantum Cohomology

Author : Joachim Kock
Publisher : Springer Science & Business Media
ISBN 13 : 0817644954
Total Pages : 162 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis An Invitation to Quantum Cohomology by : Joachim Kock

Download or read book An Invitation to Quantum Cohomology written by Joachim Kock and published by Springer Science & Business Media. This book was released on 2007-12-27 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary introduction to stable maps and quantum cohomology presents the problem of counting rational plane curves Viewpoint is mostly that of enumerative geometry Emphasis is on examples, heuristic discussions, and simple applications to best convey the intuition behind the subject Ideal for self-study, for a mini-course in quantum cohomology, or as a special topics text in a standard course in intersection theory

Geometry and Quantization of Moduli Spaces

Author : Vladimir Fock
Publisher : Birkhäuser
ISBN 13 : 3319335782
Total Pages : 220 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Geometry and Quantization of Moduli Spaces by : Vladimir Fock

Download or read book Geometry and Quantization of Moduli Spaces written by Vladimir Fock and published by Birkhäuser. This book was released on 2016-12-25 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on four advanced courses held at the Centre de Recerca Matemàtica (CRM), Barcelona. It presents both background information and recent developments on selected topics that are experiencing extraordinary growth within the broad research area of geometry and quantization of moduli spaces. The lectures focus on the geometry of moduli spaces which are mostly associated to compact Riemann surfaces, and are presented from both classical and quantum perspectives.

From Quantum Cohomology to Integrable Systems

Author : Martin A. Guest
Publisher : OUP Oxford
ISBN 13 : 0191606960
Total Pages : 336 pages
Book Rating : 4.1/5 (916 download)

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Book Synopsis From Quantum Cohomology to Integrable Systems by : Martin A. Guest

Download or read book From Quantum Cohomology to Integrable Systems written by Martin A. Guest and published by OUP Oxford. This book was released on 2008-03-13 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum cohomology has its origins in symplectic geometry and algebraic geometry, but is deeply related to differential equations and integrable systems. This text explains what is behind the extraordinary success of quantum cohomology, leading to its connections with many existing areas of mathematics as well as its appearance in new areas such as mirror symmetry. Certain kinds of differential equations (or D-modules) provide the key links between quantum cohomology and traditional mathematics; these links are the main focus of the book, and quantum cohomology and other integrable PDEs such as the KdV equation and the harmonic map equation are discussed within this unified framework. Aimed at graduate students in mathematics who want to learn about quantum cohomology in a broad context, and theoretical physicists who are interested in the mathematical setting, the text assumes basic familiarity with differential equations and cohomology.

Conférence Moshé Flato 1999

Author : Giuseppe Dito
Publisher : Springer Science & Business Media
ISBN 13 : 9401512760
Total Pages : 345 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Conférence Moshé Flato 1999 by : Giuseppe Dito

Download or read book Conférence Moshé Flato 1999 written by Giuseppe Dito and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: These two volumes constitute the Proceedings of the `Conférence Moshé Flato, 1999'. Their spectrum is wide but the various areas covered are, in fact, strongly interwoven by a common denominator, the unique personality and creativity of the scientist in whose honor the Conference was held, and the far-reaching vision that underlies his scientific activity. With these two volumes, the reader will be able to take stock of the present state of the art in a number of subjects at the frontier of current research in mathematics, mathematical physics, and physics. Volume I is prefaced by reminiscences of and tributes to Flato's life and work. It also includes a section on the applications of sciences to insurance and finance, an area which was of interest to Flato before it became fashionable. The bulk of both volumes is on physical mathematics, where the reader will find these ingredients in various combinations, fundamental mathematical developments based on them, and challenging interpretations of physical phenomena. Audience: These volumes will be of interest to researchers and graduate students in a variety of domains, ranging from abstract mathematics to theoretical physics and other applications. Some parts will be accessible to proficient undergraduate students, and even to persons with a minimum of scientific knowledge but enough curiosity.

Topology, Geometry, Integrable Systems, and Mathematical Physics

Author : V. M. Buchstaber
Publisher : American Mathematical Soc.
ISBN 13 : 1470418711
Total Pages : 393 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Topology, Geometry, Integrable Systems, and Mathematical Physics by : V. M. Buchstaber

Download or read book Topology, Geometry, Integrable Systems, and Mathematical Physics written by V. M. Buchstaber and published by American Mathematical Soc.. This book was released on 2014-11-18 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Articles in this collection are devoted to modern problems of topology, geometry, mathematical physics, and integrable systems, and they are based on talks given at the famous Novikov's seminar at the Steklov Institute of Mathematics in Moscow in 2012-2014. The articles cover many aspects of seemingly unrelated areas of modern mathematics and mathematical physics; they reflect the main scientific interests of the organizer of the seminar, Sergey Petrovich Novikov. The volume is suitable for graduate students and researchers interested in the corresponding areas of mathematics and physics.

New Developments in Singularity Theory

Author : Dirk Siersma
Publisher : Springer Science & Business Media
ISBN 13 : 9780792369967
Total Pages : 484 pages
Book Rating : 4.3/5 (699 download)

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Book Synopsis New Developments in Singularity Theory by : Dirk Siersma

Download or read book New Developments in Singularity Theory written by Dirk Siersma and published by Springer Science & Business Media. This book was released on 2001-06-30 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: Singularities arise naturally in a huge number of different areas of mathematics and science. As a consequence, singularity theory lies at the crossroads of paths that connect many of the most important areas of applications of mathematics with some of its most abstract regions. The main goal in most problems of singularity theory is to understand the dependence of some objects of analysis, geometry, physics, or other science (functions, varieties, mappings, vector or tensor fields, differential equations, models, etc.) on parameters. The articles collected here can be grouped under three headings. (A) Singularities of real maps; (B) Singular complex variables; and (C) Singularities of homomorphic maps.

Quantum Field Theory III: Gauge Theory

Author : Eberhard Zeidler
Publisher : Springer Science & Business Media
ISBN 13 : 3642224210
Total Pages : 1141 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Quantum Field Theory III: Gauge Theory by : Eberhard Zeidler

Download or read book Quantum Field Theory III: Gauge Theory written by Eberhard Zeidler and published by Springer Science & Business Media. This book was released on 2011-08-17 with total page 1141 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction. Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure. The book is arranged in four sections, devoted to realizing the universal principle force equals curvature: Part I: The Euclidean Manifold as a Paradigm Part II: Ariadne's Thread in Gauge Theory Part III: Einstein's Theory of Special Relativity Part IV: Ariadne's Thread in Cohomology For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum. Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos).

Mirror Symmetry and Algebraic Geometry

Author : David A. Cox
Publisher : American Mathematical Soc.
ISBN 13 : 082182127X
Total Pages : 469 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Mirror Symmetry and Algebraic Geometry by : David A. Cox

Download or read book Mirror Symmetry and Algebraic Geometry written by David A. Cox and published by American Mathematical Soc.. This book was released on 1999 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematicians wanting to get into the field ... will find a very well written and encyclopaedic account of the mathematics which was needed in, and was developed from, what now might be termed classical mirror symmetry. --Bulletin of the LMS The book is highly recommended for everyone who wants to learn about the fascinating recent interplay between physics and mathematics. --Mathematical Reviews Mirror symmetry began when theoretical physicists made some astonishing predictions about rational curves on quintic hypersurfaces in four-dimensional projective space. Understanding the mathematics behind these predictions has been a substantial challenge. This book is a completely comprehensive monograph on mirror symmetry, covering the original observations by the physicists through the most recent progress made to date. Subjects discussed include toric varieties, Hodge theory, Kahler geometry, moduli of stable maps, Calabi-Yau manifolds, quantum cohomology, Gromov-Witten invariants, and the mirror theorem.

The Painlevé Property

Author : Robert Conte
Publisher : Springer Science & Business Media
ISBN 13 : 1461215323
Total Pages : 828 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis The Painlevé Property by : Robert Conte

Download or read book The Painlevé Property written by Robert Conte and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 828 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Arithmetic and Geometry Around Quantization

Author : Özgür Ceyhan
Publisher : Springer Science & Business Media
ISBN 13 : 0817648313
Total Pages : 292 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Arithmetic and Geometry Around Quantization by : Özgür Ceyhan

Download or read book Arithmetic and Geometry Around Quantization written by Özgür Ceyhan and published by Springer Science & Business Media. This book was released on 2010-01-12 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises both research and survey articles originating from the conference on Arithmetic and Geometry around Quantization held in Istanbul in 2006. A wide range of topics related to quantization are covered, thus aiming to give a glimpse of a broad subject in very different perspectives.