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An Invitation to Quantum Cohomology

2007-12-27 Mathematics
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Release : 2007-12-27
Genre : Mathematics
Kind : eBook
Book Rating : 954/5 ( reviews)

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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. This book was released on 2007-12-27. 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

Quantum Cohomology

2004-10-12 Mathematics
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Release : 2004-10-12
Genre : Mathematics
Kind : eBook
Book Rating : 171/5 ( reviews)

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Book Synopsis Quantum Cohomology by : K. Behrend

Download or read book Quantum Cohomology written by K. Behrend. This book was released on 2004-10-12. Available in PDF, EPUB and Kindle. Book excerpt: The book gathers the lectures given at the C.I.M.E. summer school "Quantum Cohomology" held in Cetraro (Italy) from June 30th to July 8th, 1997. The lectures and the subsequent updating cover a large spectrum of the subject on the field, from the algebro-geometric point of view, to the symplectic approach, including recent developments of string-branes theories and q-hypergeometric functions.

From Quantum Cohomology to Integrable Systems

2008-03-13 Mathematics
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Release : 2008-03-13
Genre : Mathematics
Kind : eBook
Book Rating : 960/5 ( reviews)

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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. This book was released on 2008-03-13. 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.

$J$-Holomorphic Curves and Quantum Cohomology

1994 Mathematics
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Release : 1994
Genre : Mathematics
Kind : eBook
Book Rating : 328/5 ( reviews)

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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. This book was released on 1994. 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 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.

Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces

1999 Mathematics
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Release : 1999
Genre : Mathematics
Kind : eBook
Book Rating : 178/5 ( reviews)

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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. This book was released on 1999. 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.

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