Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces
Author | : I͡U. I. Manin |
Publisher | : American Mathematical Soc. |
Total Pages | : 330 |
Release | : |
Genre | : Mathematics |
ISBN | : 9780821874752 |
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Author | : I͡U. I. Manin |
Publisher | : American Mathematical Soc. |
Total Pages | : 330 |
Release | : |
Genre | : Mathematics |
ISBN | : 9780821874752 |
Author | : I︠U︡. I. Manin |
Publisher | : American Mathematical Soc. |
Total Pages | : 321 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : 0821819178 |
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 | : |
Total Pages | : |
Release | : 1999 |
Genre | : Homology theory |
ISBN | : 9781470431938 |
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 | : Claus Hertling |
Publisher | : Cambridge University Press |
Total Pages | : 292 |
Release | : 2002-07-25 |
Genre | : Mathematics |
ISBN | : 9780521812962 |
This book presents the theory of Frobenius manifolds, as well as all the necessary tools and several applications.
Author | : Claus Hertling |
Publisher | : Springer Science & Business Media |
Total Pages | : 384 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3322802361 |
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 | : Joachim Kock |
Publisher | : Springer Science & Business Media |
Total Pages | : 162 |
Release | : 2007-12-27 |
Genre | : Mathematics |
ISBN | : 0817644954 |
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 | : Vladimir Fock |
Publisher | : Birkhäuser |
Total Pages | : 230 |
Release | : 2016-12-25 |
Genre | : Mathematics |
ISBN | : 3319335782 |
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 | : Martin A. Guest |
Publisher | : OUP Oxford |
Total Pages | : 336 |
Release | : 2008-03-13 |
Genre | : Mathematics |
ISBN | : 0191606960 |
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 | : Giuseppe Dito |
Publisher | : Springer Science & Business Media |
Total Pages | : 345 |
Release | : 2013-03-08 |
Genre | : Mathematics |
ISBN | : 9401512760 |
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.