Read Books Online and Download eBooks, EPub, PDF, Mobi, Kindle, Text Full Free.
Classical Mirror Symmetry
Download Classical Mirror Symmetry full books in PDF, epub, and Kindle. Read online Classical Mirror Symmetry ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Book Synopsis Classical Mirror Symmetry by : Masao Jinzenji
Download or read book Classical Mirror Symmetry written by Masao Jinzenji and published by Springer. This book was released on 2018-04-18 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book furnishes a brief introduction to classical mirror symmetry, a term that denotes the process of computing Gromov–Witten invariants of a Calabi–Yau threefold by using the Picard–Fuchs differential equation of period integrals of its mirror Calabi–Yau threefold. The book concentrates on the best-known example, the quintic hypersurface in 4-dimensional projective space, and its mirror manifold.First, there is a brief review of the process of discovery of mirror symmetry and the striking result proposed in the celebrated paper by Candelas and his collaborators. Next, some elementary results of complex manifolds and Chern classes needed for study of mirror symmetry are explained. Then the topological sigma models, the A-model and the B-model, are introduced. The classical mirror symmetry hypothesis is explained as the equivalence between the correlation function of the A-model of a quintic hyper-surface and that of the B-model of its mirror manifold.On the B-model side, the process of construction of a pair of mirror Calabi–Yau threefold using toric geometry is briefly explained. Also given are detailed explanations of the derivation of the Picard–Fuchs differential equation of the period integrals and on the process of deriving the instanton expansion of the A-model Yukawa coupling based on the mirror symmetry hypothesis.On the A-model side, the moduli space of degree d quasimaps from CP^1 with two marked points to CP^4 is introduced, with reconstruction of the period integrals used in the B-model side as generating functions of the intersection numbers of the moduli space. Lastly, a mathematical justification for the process of the B-model computation from the point of view of the geometry of the moduli space of quasimaps is given.The style of description is between that of mathematics and physics, with the assumption that readers have standard graduate student backgrounds in both disciplines.
Download or read book Mirror Symmetry written by Kentaro Hori and published by American Mathematical Soc.. This book was released on 2003 with total page 954 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thorough and detailed exposition is the result of an intensive month-long course on mirror symmetry sponsored by the Clay Mathematics Institute. It develops mirror symmetry from both mathematical and physical perspectives with the aim of furthering interaction between the two fields. The material will be particularly useful for mathematicians and physicists who wish to advance their understanding across both disciplines. Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics. Such a correspondence has significant mathematical consequences, the most familiar of which involves the enumeration of holomorphic curves inside complex manifolds by solving differential equations obtained from a ``mirror'' geometry. The inclusion of D-brane states in the equivalence has led to further conjectures involving calibrated submanifolds of the mirror pairs and new (conjectural) invariants of complex manifolds: the Gopakumar-Vafa invariants. This book gives a single, cohesive treatment of mirror symmetry. Parts 1 and 2 develop the necessary mathematical and physical background from ``scratch''. The treatment is focused, developing only the material most necessary for the task. In Parts 3 and 4 the physical and mathematical proofs of mirror symmetry are given. From the physics side, this means demonstrating that two different physical theories give isomorphic physics. Each physical theory can be described geometrically, and thus mirror symmetry gives rise to a ``pairing'' of geometries. The proof involves applying $R\leftrightarrow 1/R$ circle duality to the phases of the fields in the gauged linear sigma model. The mathematics proof develops Gromov-Witten theory in the algebraic setting, beginning with the moduli spaces of curves and maps, and uses localization techniques to show that certain hypergeometric functions encode the Gromov-Witten invariants in genus zero, as is predicted by mirror symmetry. Part 5 is devoted to advanced topi This one-of-a-kind book is suitable for graduate students and research mathematicians interested in mathematics and mathematical and theoretical physics.
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 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 the first 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. This title features: numerous examples worked out in detail; an appendix on mathematical physics; an exposition of the algebraic theory of Gromov-Witten invariants and quantum cohomology; and, a proof of the mirror theorem for the quintic threefold.
Book Synopsis Tropical Geometry and Mirror Symmetry by : Mark Gross
Download or read book Tropical Geometry and Mirror Symmetry written by Mark Gross and published by American Mathematical Soc.. This book was released on 2011-01-20 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tropical geometry provides an explanation for the remarkable power of mirror symmetry to connect complex and symplectic geometry. The main theme of this book is the interplay between tropical geometry and mirror symmetry, culminating in a description of the recent work of Gross and Siebert using log geometry to understand how the tropical world relates the A- and B-models in mirror symmetry. The text starts with a detailed introduction to the notions of tropical curves and manifolds, and then gives a thorough description of both sides of mirror symmetry for projective space, bringing together material which so far can only be found scattered throughout the literature. Next follows an introduction to the log geometry of Fontaine-Illusie and Kato, as needed for Nishinou and Siebert's proof of Mikhalkin's tropical curve counting formulas. This latter proof is given in the fourth chapter. The fifth chapter considers the mirror, B-model side, giving recent results of the author showing how tropical geometry can be used to evaluate the oscillatory integrals appearing. The final chapter surveys reconstruction results of the author and Siebert for ``integral tropical manifolds.'' A complete version of the argument is given in two dimensions.
Book Synopsis Dirichlet Branes and Mirror Symmetry by :
Download or read book Dirichlet Branes and Mirror Symmetry written by and published by American Mathematical Soc.. This book was released on 2009 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research in string theory has generated a rich interaction with algebraic geometry, with exciting work that includes the Strominger-Yau-Zaslow conjecture. This monograph builds on lectures at the 2002 Clay School on Geometry and String Theory that sought to bridge the gap between the languages of string theory and algebraic geometry.
Book Synopsis Symmetry: A Very Short Introduction by : Ian Stewart
Download or read book Symmetry: A Very Short Introduction written by Ian Stewart and published by OUP Oxford. This book was released on 2013-05-30 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 1800s mathematicians introduced a formal theory of symmetry: group theory. Now a branch of abstract algebra, this subject first arose in the theory of equations. Symmetry is an immensely important concept in mathematics and throughout the sciences, and its applications range across the entire subject. Symmetry governs the structure of crystals, innumerable types of pattern formation, how systems change their state as parameters vary; and fundamental physics is governed by symmetries in the laws of nature. It is highly visual, with applications that include animal markings, locomotion, evolutionary biology, elastic buckling, waves, the shape of the Earth, and the form of galaxies. In this Very Short Introduction, Ian Stewart demonstrates its deep implications, and shows how it plays a major role in the current search to unify relativity and quantum theory. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
Book Synopsis Mirror Symmetry I by : Shing-Tung Yau
Download or read book Mirror Symmetry I written by Shing-Tung Yau and published by American Mathematical Soc.. This book was released on 1998 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vol. 1 represents a new ed. of papers which were originally published in Essays on mirror manifolds (1992); supplemented by the additional volume: Mirror symmetry 2 which presents papers by both physicists and mathematicians. Mirror symmetry 1 (the 1st volume) constitutes the proceedings of the Mathematical Sciences Research Institute Workshop of 1991.
Book Synopsis J-holomorphic Curves and Symplectic Topology by : Dusa McDuff
Download or read book J-holomorphic Curves and Symplectic Topology written by Dusa McDuff and published by American Mathematical Soc.. This book was released on 2012 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of this book is to establish the fundamental theorems of the subject in full and rigourous detail. In particular, the book contains complete proofs of Gromov's compactness theorem for spheres, of the gluing theorem for spheres, and of the associatively of quantum multiplication in the semipositive case. The book can also serve as an introduction to current work in symplectic topology.
Book Synopsis Partition Functions and Automorphic Forms by : Valery A. Gritsenko
Download or read book Partition Functions and Automorphic Forms written by Valery A. Gritsenko and published by Springer Nature. This book was released on 2020-07-09 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to the research in several recently discovered and actively developing mathematical and mathematical physics areas. It focuses on: 1) Feynman integrals and modular functions, 2) hyperbolic and Lorentzian Kac-Moody algebras, related automorphic forms and applications to quantum gravity, 3) superconformal indices and elliptic hypergeometric integrals, related instanton partition functions, 4) moonshine, its arithmetic aspects, Jacobi forms, elliptic genus, and string theory, and 5) theory and applications of the elliptic Painleve equation, and aspects of Painleve equations in quantum field theories. All the topics covered are related to various partition functions emerging in different supersymmetric and ordinary quantum field theories in curved space-times of different (d=2,3,...,6) dimensions. Presenting multidisciplinary methods (localization, Borcherds products, theory of special functions, Cremona maps, etc) for treating a range of partition functions, the book is intended for graduate students and young postdocs interested in the interaction between quantum field theory and mathematics related to automorphic forms, representation theory, number theory and geometry, and mirror symmetry.
Book Synopsis The Unity of Mathematics by : Pavel Etingof
Download or read book The Unity of Mathematics written by Pavel Etingof and published by Springer Science & Business Media. This book was released on 2007-05-31 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tribute to the vision and legacy of Israel Moiseevich Gel'fand Written by leading mathematicians, these invited papers reflect the unity of mathematics as a whole, with particular emphasis on the many connections among the fields of geometry, physics, and representation theory Topics include conformal field theory, K-theory, noncommutative geometry, gauge theory, representations of infinite-dimensional Lie algebras, and various aspects of the Langlands program
Book Synopsis Classical Algebraic Geometry by : Igor V. Dolgachev
Download or read book Classical Algebraic Geometry written by Igor V. Dolgachev and published by Cambridge University Press. This book was released on 2012-08-16 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic geometry has benefited enormously from the powerful general machinery developed in the latter half of the twentieth century. The cost has been that much of the research of previous generations is in a language unintelligible to modern workers, in particular, the rich legacy of classical algebraic geometry, such as plane algebraic curves of low degree, special algebraic surfaces, theta functions, Cremona transformations, the theory of apolarity and the geometry of lines in projective spaces. The author's contemporary approach makes this legacy accessible to modern algebraic geometers and to others who are interested in applying classical results. The vast bibliography of over 600 references is complemented by an array of exercises that extend or exemplify results given in the book.
Book Synopsis Color and Symmetry by : Arthur Lee Loeb
Download or read book Color and Symmetry written by Arthur Lee Loeb and published by . This book was released on 1978 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Symmetry and the Beautiful Universe by : Leon M. Lederman
Download or read book Symmetry and the Beautiful Universe written by Leon M. Lederman and published by Prometheus Books. This book was released on 2011-11-29 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: When scientists peer through a telescope at the distant stars in outer space or use a particle-accelerator to analyze the smallest components of matter, they discover that the same laws of physics govern the whole universe at all times and all places. Physicists call the eternal, ubiquitous constancy of the laws of physics symmetry. Symmetry is the basic underlying principle that defines the laws of nature and hence controls the universe. This all-important insight is one of the great conceptual breakthroughs in modern physics and is the basis of contemporary efforts to discover a grand unified theory to explain all the laws of physics. Nobel Laureate Leon M. Lederman and physicist Christopher T. Hill explain the supremely elegant concept of symmetry and all its profound ramifications to life on Earth and the universe at large in this eloquent, accessible popular science book. They not only clearly describe concepts normally reserved only for physicists and mathematicians, but they also instill an appreciation for the profound beauty of the universe’s inherent design. Central to the story of symmetry is an obscure, unpretentious, but extremely gifted German mathematician named Emmy Noether. Though still little known to the world, she impressed no less a scientist than Albert Einstein, who praised her "penetrating mathematical thinking." In some of her earliest work she proved that the law of the conservation of energy was connected to the idea of symmetry and thus laid the mathematical groundwork for what may be the most important concept of modern physics. Lederman and Hill reveal concepts about the universe, based on Noether’s work, that are largely unknown to the public and have wide-reaching implications in connection with the Big Bang, Einstein’s theory of relativity, quantum mechanics, and many other areas of physics. Through ingenious analogies and illustrations, they bring these astounding notions to life. This book will open your eyes to a universe you never knew existed.
Book Synopsis Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory by : Johannes Blümlein
Download or read book Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory written by Johannes Blümlein and published by Springer. This book was released on 2019-01-30 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes review articles in the field of elliptic integrals, elliptic functions and modular forms intending to foster the discussion between theoretical physicists working on higher loop calculations and mathematicians working in the field of modular forms and functions and analytic solutions of higher order differential and difference equations.
Book Synopsis Singularities, Mirror Symmetry, and the Gauged Linear Sigma Model by : Tyler J. Jarvis
Download or read book Singularities, Mirror Symmetry, and the Gauged Linear Sigma Model written by Tyler J. Jarvis and published by American Mathematical Society. This book was released on 2021-02-26 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the workshop Crossing the Walls in Enumerative Geometry, held in May 2018 at Snowbird, Utah. It features a collection of both expository and research articles about mirror symmetry, quantized singularity theory (FJRW theory), and the gauged linear sigma model. Most of the expository works are based on introductory lecture series given at the workshop and provide an approachable introduction for graduate students to some fundamental topics in mirror symmetry and singularity theory, including quasimaps, localization, the gauged linear sigma model (GLSM), virtual classes, cosection localization, $p$-fields, and Saito's primitive forms. These articles help readers bridge the gap from the standard graduate curriculum in algebraic geometry to exciting cutting-edge research in the field. The volume also contains several research articles by leading researchers, showcasing new developments in the field.
Book Synopsis Symmetries in Physics by : Katherine Brading
Download or read book Symmetries in Physics written by Katherine Brading and published by Cambridge University Press. This book was released on 2003-12-04 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together philosophical discussions of symmetry in physics, highlighting the main issues and controversies. It covers all the fundamental symmetries of modern physics, as well as discussing symmetry-breaking and general interpretational issues. For each topic, classic texts are followed by review articles and short commentaries.
Book Synopsis Gromov-Witten Theory of Quotients of Fermat Calabi-Yau Varieties by : Hiroshi Iritani
Download or read book Gromov-Witten Theory of Quotients of Fermat Calabi-Yau Varieties written by Hiroshi Iritani and published by American Mathematical Soc.. This book was released on 2021-06-21 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gromov-Witten theory started as an attempt to provide a rigorous mathematical foundation for the so-called A-model topological string theory of Calabi-Yau varieties. Even though it can be defined for all the Kähler/symplectic manifolds, the theory on Calabi-Yau varieties remains the most difficult one. In fact, a great deal of techniques were developed for non-Calabi-Yau varieties during the last twenty years. These techniques have only limited bearing on the Calabi-Yau cases. In a certain sense, Calabi-Yau cases are very special too. There are two outstanding problems for the Gromov-Witten theory of Calabi-Yau varieties and they are the focus of our investigation.
