Frobenius Manifolds Quantum Cohomology And Moduli Spaces
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Frobenius Manifolds Quantum Cohomology And Moduli Spaces
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Author : I︠U︡. I. Manin
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Frobenius Manifolds Quantum Cohomology And Moduli Spaces written by I︠U︡. I. Manin 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 1999 with Mathematics categories.
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
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Author : I︠U︡. I. Manin
language : en
Publisher:
Release Date : 1999
Frobenius Manifolds Quantum Cohomology And Moduli Spaces written by I︠U︡. I. Manin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Homology theory categories.
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 Chapters I Ii Iii
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Author : Yu. I. Manin
language : en
Publisher:
Release Date : 1996
Frobenius Manifolds Quantum Cohomology And Moduli Spaces Chapters I Ii Iii written by Yu. I. Manin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
Frobenius Manifolds And Moduli Spaces For Singularities
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Author : Claus Hertling
language : en
Publisher: Cambridge University Press
Release Date : 2002-07-25
Frobenius Manifolds And Moduli Spaces For Singularities written by Claus Hertling 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 2002-07-25 with Mathematics categories.
This book presents the theory of Frobenius manifolds, as well as all the necessary tools and several applications.
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.
Geometry And Quantization Of Moduli Spaces
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Author : Vladimir Fock
language : en
Publisher: Birkhäuser
Release Date : 2016-12-25
Geometry And Quantization Of Moduli Spaces written by Vladimir Fock and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-25 with Mathematics categories.
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.
Conf Rence Mosh Flato 1999
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Author : Giuseppe Dito
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-08
Conf Rence Mosh Flato 1999 written by Giuseppe Dito 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 2013-03-08 with Mathematics categories.
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.
Symplectic Geometry And Mirror Symmetry Proceedings Of The 4th Kias Annual International Conference
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Author : Kenji Fukaya
language : en
Publisher: World Scientific
Release Date : 2001-11-19
Symplectic Geometry And Mirror Symmetry Proceedings Of The 4th Kias Annual International Conference written by Kenji Fukaya and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-11-19 with Mathematics categories.
In 1993, M Kontsevich proposed a conceptual framework for explaining the phenomenon of mirror symmetry. Mirror symmetry had been discovered by physicists in string theory as a duality between families of three-dimensional Calabi-Yau manifolds. Kontsevich's proposal uses Fukaya's construction of the A∞-category of Lagrangian submanifolds on the symplectic side and the derived category of coherent sheaves on the complex side. The theory of mirror symmetry was further enhanced by physicists in the language of D-branes and also by Strominger-Yau-Zaslow in the geometric set-up of (special) Lagrangian torus fibrations. It rapidly expanded its scope across from geometry, topology, algebra to physics.In this volume, leading experts in the field explore recent developments in relation to homological mirror symmetry, Floer theory, D-branes and Gromov-Witten invariants. Kontsevich-Soibelman describe their solution to the mirror conjecture on the abelian variety based on the deformation theory of A∞-categories, and Ohta describes recent work on the Lagrangian intersection Floer theory by Fukaya-Oh-Ohta-Ono which takes an important step towards a rigorous construction of the A∞-category. There follow a number of contributions on the homological mirror symmetry, D-branes and the Gromov-Witten invariants, e.g. Getzler shows how the Toda conjecture follows from recent work of Givental, Okounkov and Pandharipande. This volume provides a timely presentation of the important developments of recent years in this rapidly growing field.
Quantum Field Theory I Basics In Mathematics And Physics
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Author : Eberhard Zeidler
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-18
Quantum Field Theory I Basics In Mathematics And Physics written by Eberhard Zeidler 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 2007-04-18 with Science categories.
This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics.
New Developments In Singularity Theory
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Author : Dirk Siersma
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-06-30
New Developments In Singularity Theory written by Dirk Siersma 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 2001-06-30 with Mathematics categories.
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.