Mirror Symmetry Ii
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Mirror Symmetry Ii
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Author : Brian Greene
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Mirror Symmetry Ii written by Brian Greene 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 1997 with Mathematics categories.
Mirror Symmetry has undergone dramatic progress since the Mathematical Sciences Research Institute (MSRI) workshop in 1991, whose proceedings constitute voluem I of this continuing collection. Tremendous insight has been gained on a number of key issues. This volume surveys these results. Some of the contributions in this work have appeared elsewhere, while others were written specifically for this collection. The areas covered are organized into 4 sections, and each presents papers by both physicists and mathematicians. This volume collects the most important developments that have taken place in mathematical physics since 1991. It is an essential reference tool for both mathematics and physics libraries and for students of physics and mathematics. Titles in this series are co-published, between the American Mathematical Society and International Press, Cambridge, MA, USA.
Homological Mirror Symmetry
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Author : Anton Kapustin
language : en
Publisher: Springer Science & Business Media
Release Date : 2009
Homological Mirror Symmetry written by Anton Kapustin 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 2009 with Mathematics categories.
An ideal reference on the mathematical aspects of quantum field theory, this volume provides a set of lectures and reviews that both introduce and representatively review the state-of-the art in the field from different perspectives.
Symplectic Geometry And Mirror Symmetry
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Author : Kenji Fukaya
language : en
Publisher: World Scientific
Release Date : 2001
Symplectic Geometry And Mirror Symmetry 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 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 Aì-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 Aì-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 Aì-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.
Tropical Geometry And Mirror Symmetry
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Author : Mark Gross
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-01-20
Tropical Geometry And Mirror Symmetry written by Mark Gross 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 2011-01-20 with Mathematics categories.
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.
Dirichlet Branes And Mirror Symmetry
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Author :
language : en
Publisher: American Mathematical Soc.
Release Date :
Dirichlet Branes And Mirror Symmetry written by 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 with categories.
The Moduli Space Of Curves
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Author : R. Dijkgraaf
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-10-18
The Moduli Space Of Curves written by R. Dijkgraaf 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 1995-10-18 with Mathematics categories.
The moduli space Mg of curves of fixed genus g – that is, the algebraic variety that parametrizes all curves of genus g – is one of the most intriguing objects of study in algebraic geometry these days. Its appeal results not only from its beautiful mathematical structure but also from recent developments in theoretical physics, in particular in conformal field theory. Leading experts in the field explore in this volume both the structure of the moduli space of curves and its relationship with physics through quantum cohomology. Altogether, this is a lively volume that testifies to the ferment in the field and gives an excellent view of the state of the art for both mathematicians and theoretical physicists. It is a persuasive example of the famous Wignes comment, and its converse, on "the unreasonable effectiveness of mathematics in the natural science." Witteen’s conjecture in 1990 describing the intersection behavior of tautological classes in the cohomology of Mg arose directly from string theory. Shortly thereafter a stunning proof was provided by Kontsevich who, in this volume, describes his solution to the problem of counting rational curves on certain algebraic varieties and includes numerous suggestions for further development. The same problem is given an elegant treatment in a paper by Manin. There follows a number of contributions to the geometry, cohomology, and arithmetic of the moduli spaces of curves. In addition, several contributors address quantum cohomology and conformal field theory.
Visual Symmetry
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Author : Magdolna Hargittai
language : en
Publisher: World Scientific
Release Date : 2009
Visual Symmetry written by Magdolna Hargittai and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
Symmetry is as simple or as complicated as we are ready to absorb it in everything around us. From flowers to bridges, buildings, coke machines, and snowflakes; from molecules to walnuts, fences, pine cones, and sunflowers; from music to children's drawings; from hubcaps to bank logos, propellers, wallpaper decorations, and pavements, we recognize it if we walk around with open eyes and an open mind. This book provides aesthetic pleasure and covert education, immersing the reader in both the familiar and the unknown and leading always to unexpected discoveries. The authors, world-renowned scientists, have already produced a dozen books on symmetry for professionals as well as laypersons, for grownups as well as children, in English, Russian, German, Hungarian, and Swedish languages. They provide this attractive account of symmetry in few words and many ? as many as 650 ? images in full color from the most diverse corners of our globe. An encounter with this book will open up a whole new experience for the reader, who will never look at the world with the same eyes as before.
Minimal Surfaces Geometric Analysis And Symplectic Geometry
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Author : Kenji Fukaya
language : en
Publisher:
Release Date : 2002
Minimal Surfaces Geometric Analysis And Symplectic Geometry written by Kenji Fukaya and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
The 1998-1999 programme year of the Japan-U.S. Mathematics Institute at the Johns Hopkins University, USA was devoted to minimal surfaces, geometric analysis, and symplectic geometry. The programme culminated in a week-long workshop and conference to discuss developments. This volume is a collection of articles written by the speakers. It presents extended or modified versions of the lectures delivered at the meeting. Each article provides a vivid account of contemporary research, with the information given ranging from introductory level to the most up-to-date results. Of special interest is a long survey article by K. Fukaya on applications of Floer homology to mirror symmetry. Also discussed are developments on the geometry of constant mean curvature one surfaces in hyperbolic 3-spaces of finite total curvature. The range of topics covered in the volume provides direction for further research in these rapidly developing areas. The book should be suitable for graduate students and researchers interested in differential and symplectic geometry.
Homological Mirror Symmetry And Tropical Geometry
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Author : Ricardo Castano-Bernard
language : en
Publisher: Springer
Release Date : 2014-10-16
Homological Mirror Symmetry And Tropical Geometry written by Ricardo Castano-Bernard and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-16 with Mathematics categories.
The relationship between Tropical Geometry and Mirror Symmetry goes back to the work of Kontsevich and Y. Soibelman (2000), who applied methods of non-archimedean geometry (in particular, tropical curves) to Homological Mirror Symmetry. In combination with the subsequent work of Mikhalkin on the “tropical” approach to Gromov-Witten theory and the work of Gross and Siebert, Tropical Geometry has now become a powerful tool. Homological Mirror Symmetry is the area of mathematics concentrated around several categorical equivalences connecting symplectic and holomorphic (or algebraic) geometry. The central ideas first appeared in the work of Maxim Kontsevich (1993). Roughly speaking, the subject can be approached in two ways: either one uses Lagrangian torus fibrations of Calabi-Yau manifolds (the so-called Strominger-Yau-Zaslow picture, further developed by Kontsevich and Soibelman) or one uses Lefschetz fibrations of symplectic manifolds (suggested by Kontsevich and further developed by Seidel). Tropical Geometry studies piecewise-linear objects which appear as “degenerations” of the corresponding algebro-geometric objects.
Symmetry 2
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Author : I. Hargittai
language : en
Publisher: Elsevier
Release Date : 2016-02-25
Symmetry 2 written by I. Hargittai and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-25 with Mathematics categories.
Symmetry 2 aims to present an overview of the contemporary status of symmetry studies, particularly in the arts and sciences, emphasizing both its role and importance. Symmetry is not only one of the fundamental concepts in science, but is also possibly the best unifying concept between various branches of science, the arts and other human activities. Whereas symmetry has been considered important for centuries primarily for its aesthetic appeal, this century has witnessed a dramatic enhancement of its status as a cornerstone in the sciences. In addition to traditionally symmetry-oriented fields such as crystallography and spectroscopy, the concept has made headway in fields as varied as reaction chemistry, nuclear physics, and the study of the origin of the universe. The book was initiated in response to the success of the first volume, which not only received good reviews, but received the award for "The Best Single Issue of a Journal" by the Association of American Publishers for 1986. The second volume extends the application of symmetry to new fields, such as medical sciences and economics, as well as investigating further certain topics introduced in Symmetry. The book is extensively illustrated and with over 64 contributions from 16 countries presents an international overview of the nature and diversity of symmetry studies today.