Frobenius Manifolds Quantum Cohomology And Moduli Spaces

Author : I︠U︡. I. Manin,Yuri I. Manin,︠I︡U. I. Manin
Publisher : American Mathematical Soc.
Page : 321 pages
File Size : 40,6 Mb
Release : 1999
Category : Cohomology operations
ISBN : 9780821819173

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Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces by I︠U︡. I. Manin,Yuri I. Manin,︠I︡U. I. Manin Pdf

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.

Author : I︠U︡. I. Manin
Publisher : Unknown
Page : 128 pages
File Size : 46,8 Mb
Release : 1999
Category : Homology theory
ISBN : 1470431939

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Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces by I︠U︡. I. Manin Pdf

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.

Author : I͡U. I. Manin
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 49,9 Mb
Release : 2024-06-29
Category : Mathematics
ISBN : 0821874756

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Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces by I͡U. I. Manin Pdf

Author : Claus Hertling,Matilde Marcolli
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 49,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783322802361

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Frobenius Manifolds by Claus Hertling,Matilde Marcolli Pdf

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.

Author : Claus Hertling
Publisher : Cambridge University Press
Page : 292 pages
File Size : 48,7 Mb
Release : 2002-07-25
Category : Mathematics
ISBN : 0521812968

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Frobenius Manifolds and Moduli Spaces for Singularities by Claus Hertling Pdf

This book presents the theory of Frobenius manifolds, as well as all the necessary tools and several applications.

Author : Ralph M. Kaufmann
Publisher : Unknown
Page : 106 pages
File Size : 51,5 Mb
Release : 1998
Category : Curves
ISBN : UOM:39015055824679

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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 Pdf

Author : Joachim Kock,Israel Vainsencher
Publisher : Springer Science & Business Media
Page : 162 pages
File Size : 45,6 Mb
Release : 2007-12-27
Category : Mathematics
ISBN : 9780817644956

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An Invitation to Quantum Cohomology by Joachim Kock,Israel Vainsencher Pdf

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

Author : Dusa McDuff,Dietmar Salamon
Publisher : American Mathematical Soc.
Page : 220 pages
File Size : 54,5 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821803325

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$J$-Holomorphic Curves and Quantum Cohomology by Dusa McDuff,Dietmar Salamon Pdf

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 the quantum multiplication exists and 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 Grassmanians, which relates to the Verlinde algebra. The Dubrovin connection, Gromov-Witten potential on quantum cohomology, and curve counting formulas are also discussed.

Author : Martin A. Guest
Publisher : OUP Oxford
Page : 336 pages
File Size : 51,6 Mb
Release : 2008-03-13
Category : Mathematics
ISBN : 9780191606960

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From Quantum Cohomology to Integrable Systems by Martin A. Guest Pdf

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.

Author : Vladimir Fock,Andrey Marshakov,Florent Schaffhauser,Constantin Teleman,Richard Wentworth
Publisher : Birkhäuser
Page : 220 pages
File Size : 40,6 Mb
Release : 2016-12-25
Category : Mathematics
ISBN : 9783319335780

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Geometry and Quantization of Moduli Spaces by Vladimir Fock,Andrey Marshakov,Florent Schaffhauser,Constantin Teleman,Richard Wentworth Pdf

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.

Author : Giuseppe Dito,Daniel Sternheimer
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 45,5 Mb
Release : 2013-03-08
Category : Mathematics
ISBN : 9789401512763

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Conférence Moshé Flato 1999 by Giuseppe Dito,Daniel Sternheimer Pdf

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.

Author : V. M. Buchstaber,B. A. Dubrovin, I. M. Krichever
Publisher : American Mathematical Soc.
Page : 408 pages
File Size : 42,7 Mb
Release : 2014-11-18
Category : Mathematics
ISBN : 9781470418717

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Topology, Geometry, Integrable Systems, and Mathematical Physics by V. M. Buchstaber,B. A. Dubrovin, I. M. Krichever Pdf

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.

Author : Dirk Siersma,Charles Wall,V. Zakalyukin
Publisher : Springer Science & Business Media
Page : 484 pages
File Size : 43,6 Mb
Release : 2001-06-30
Category : Mathematics
ISBN : 0792369963

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New Developments in Singularity Theory by Dirk Siersma,Charles Wall,V. Zakalyukin Pdf

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.

Author : Eberhard Zeidler
Publisher : Springer Science & Business Media
Page : 1141 pages
File Size : 50,7 Mb
Release : 2011-08-17
Category : Mathematics
ISBN : 9783642224218

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Quantum Field Theory III: Gauge Theory by Eberhard Zeidler Pdf

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).

Author : David A. Cox,Sheldon Katz
Publisher : American Mathematical Soc.
Page : 469 pages
File Size : 53,7 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821821275

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Mirror Symmetry and Algebraic Geometry by David A. Cox,Sheldon Katz Pdf

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.