Symplectic Geometry and Mirror Symmetry

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Publisher : World Scientific
ISBN 13 : 9810247141
Total Pages : 510 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Symplectic Geometry and Mirror Symmetry by : Kenji Fukaya

Download or read book Symplectic Geometry and Mirror Symmetry written by Kenji Fukaya and published by World Scientific. This book was released on 2001 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Symplectic Geometry And Mirror Symmetry - Proceedings Of The 4th Kias Annual International Conference

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Publisher : World Scientific
ISBN 13 : 9814490407
Total Pages : 510 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Symplectic Geometry And Mirror Symmetry - Proceedings Of The 4th Kias Annual International Conference by : Kenji Fukaya

Download or read book Symplectic Geometry And Mirror Symmetry - Proceedings Of The 4th Kias Annual International Conference written by Kenji Fukaya and published by World Scientific. This book was released on 2001-11-19 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 A∞-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 A∞-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 A∞-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.

Symplectic Geometry and Mirror Symmetry

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Publisher :
ISBN 13 :
Total Pages : 498 pages
Book Rating : 4.:/5 (248 download)

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Book Synopsis Symplectic Geometry and Mirror Symmetry by : Korea Institute for Advanced Study

Download or read book Symplectic Geometry and Mirror Symmetry written by Korea Institute for Advanced Study and published by . This book was released on 2001 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Symplectic Geometry and Mirror Symmetry

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Publisher : World Scientific
ISBN 13 : 9789812799821
Total Pages : 940 pages
Book Rating : 4.7/5 (998 download)

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Book Synopsis Symplectic Geometry and Mirror Symmetry by : Kodŭng Kwahagwŏn (Korea). International Conference

Download or read book Symplectic Geometry and Mirror Symmetry written by Kodŭng Kwahagwŏn (Korea). International Conference and published by World Scientific. This book was released on 2001 with total page 940 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 A∞-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 A∞-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 A∞-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.

Calabi-Yau Manifolds and Related Geometries

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Publisher : Springer Science & Business Media
ISBN 13 : 3642190049
Total Pages : 245 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Calabi-Yau Manifolds and Related Geometries by : Mark Gross

Download or read book Calabi-Yau Manifolds and Related Geometries written by Mark Gross and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to a very active field of research, on the boundary between mathematics and physics. It is aimed at graduate students and researchers in geometry and string theory. Proofs or sketches are given for many important results. From the reviews: "An excellent introduction to current research in the geometry of Calabi-Yau manifolds, hyper-Kähler manifolds, exceptional holonomy and mirror symmetry....This is an excellent and useful book." --MATHEMATICAL REVIEWS

Algebra, Geometry, and Physics in the 21st Century

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Publisher : Birkhäuser
ISBN 13 : 3319599399
Total Pages : 364 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Algebra, Geometry, and Physics in the 21st Century by : Denis Auroux

Download or read book Algebra, Geometry, and Physics in the 21st Century written by Denis Auroux and published by Birkhäuser. This book was released on 2017-07-27 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a tribute to Maxim Kontsevich, one of the most original and influential mathematicians of our time. Maxim’s vision has inspired major developments in many areas of mathematics, ranging all the way from probability theory to motives over finite fields, and has brought forth a paradigm shift at the interface of modern geometry and mathematical physics. Many of his papers have opened completely new directions of research and led to the solutions of many classical problems. This book collects papers by leading experts currently engaged in research on topics close to Maxim’s heart. Contributors: S. Donaldson A. Goncharov D. Kaledin M. Kapranov A. Kapustin L. Katzarkov A. Noll P. Pandit S. Pimenov J. Ren P. Seidel C. Simpson Y. Soibelman R. Thorngren

Toric Topology

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Publisher : American Mathematical Soc.
ISBN 13 : 0821844865
Total Pages : 424 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Toric Topology by : International Conference on Toric Topology

Download or read book Toric Topology written by International Conference on Toric Topology and published by American Mathematical Soc.. This book was released on 2008 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Toric topology is the study of algebraic, differential, symplectic-geometric, combinatorial, and homotopy-theoretic aspects of a particular class of torus actions whose quotients are highly structured. The combinatorial properties of this quotient and the equivariant topology of the original manifold interact in a rich variety of ways, thus illuminating subtle aspects of both the combinatorics and the equivariant topology. Many of the motivations and guiding principles of the fieldare provided by (though not limited to) the theory of toric varieties in algebraic geometry as well as that of symplectic toric manifolds in symplectic geometry.This volume is the proceedings of the International Conference on Toric Topology held in Osaka in May-June 2006. It contains about 25 research and survey articles written by conference speakers, covering many different aspects of, and approaches to, torus actions, such as those mentioned above. Some of the manuscripts are survey articles, intended to give a broad overview of an aspect of the subject; all manuscripts consciously aim to be accessible to a broad reading audience of students andresearchers interested in the interaction of the subjects involved. We hope that this volume serves as an enticing invitation to this emerging field.

Riemannian Holonomy Groups and Calibrated Geometry

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Publisher : Oxford University Press
ISBN 13 : 019921560X
Total Pages : 314 pages
Book Rating : 4.1/5 (992 download)

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Book Synopsis Riemannian Holonomy Groups and Calibrated Geometry by : Dominic D. Joyce

Download or read book Riemannian Holonomy Groups and Calibrated Geometry written by Dominic D. Joyce and published by Oxford University Press. This book was released on 2007 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering an exciting and active area of research at the crossroads of several different fields in mathematics and physics, and drawing on the author's previous work, this text has been written to explain the advanced mathematics involved simply and clearly to graduate students in both disciplines.

Deformation Spaces

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Publisher : Springer Science & Business Media
ISBN 13 : 3834896802
Total Pages : 173 pages
Book Rating : 4.8/5 (348 download)

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Book Synopsis Deformation Spaces by : Hossein Abbaspour

Download or read book Deformation Spaces written by Hossein Abbaspour and published by Springer Science & Business Media. This book was released on 2010-04-21 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first instances of deformation theory were given by Kodaira and Spencer for complex structures and by Gerstenhaber for associative algebras. Since then, deformation theory has been applied as a useful tool in the study of many other mathematical structures, and even today it plays an important role in many developments of modern mathematics. This volume collects a few self-contained and peer-reviewed papers by experts which present up-to-date research topics in algebraic and motivic topology, quantum field theory, algebraic geometry, noncommutative geometry and the deformation theory of Poisson algebras. They originate from activities at the Max-Planck-Institute for Mathematics and the Hausdorff Center for Mathematics in Bonn.

Lagrangian Floer Theory and Its Deformations

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Publisher : Springer Nature
ISBN 13 : 9819717981
Total Pages : 426 pages
Book Rating : 4.8/5 (197 download)

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Book Synopsis Lagrangian Floer Theory and Its Deformations by : Yong-Geun Oh

Download or read book Lagrangian Floer Theory and Its Deformations written by Yong-Geun Oh and published by Springer Nature. This book was released on with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fukaya Categories and Picard-Lefschetz Theory

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Publisher : European Mathematical Society
ISBN 13 : 9783037190630
Total Pages : 340 pages
Book Rating : 4.1/5 (96 download)

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Book Synopsis Fukaya Categories and Picard-Lefschetz Theory by : Paul Seidel

Download or read book Fukaya Categories and Picard-Lefschetz Theory written by Paul Seidel and published by European Mathematical Society. This book was released on 2008 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central objects in the book are Lagrangian submanifolds and their invariants, such as Floer homology and its multiplicative structures, which together constitute the Fukaya category. The relevant aspects of pseudo-holomorphic curve theory are covered in some detail, and there is also a self-contained account of the necessary homological algebra. Generally, the emphasis is on simplicity rather than generality. The last part discusses applications to Lefschetz fibrations and contains many previously unpublished results. The book will be of interest to graduate students and researchers in symplectic geometry and mirror symmetry.

Algebraic Geometry

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Publisher : American Mathematical Soc.
ISBN 13 : 0821847023
Total Pages : 506 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Algebraic Geometry by : Dan Abramovich

Download or read book Algebraic Geometry written by Dan Abramovich and published by American Mathematical Soc.. This book was released on 2009 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains research and expository papers by some of the speakers at the 2005 AMS Summer Institute on Algebraic Geometry. Numerous papers delve into the geometry of various moduli spaces, including those of stable curves, stable maps, coherent sheaves, and abelian varieties.

Doga. Türk matematik dergisi

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Publisher :
ISBN 13 :
Total Pages : 634 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Doga. Türk matematik dergisi by :

Download or read book Doga. Türk matematik dergisi written by and published by . This book was released on 2003 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Reviews

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Publisher :
ISBN 13 :
Total Pages : 732 pages
Book Rating : 4.X/5 (6 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2002 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mirror Symmetry IV

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Publisher : American Mathematical Soc.
ISBN 13 : 0821833359
Total Pages : 394 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Mirror Symmetry IV by : Eric D'Hoker

Download or read book Mirror Symmetry IV written by Eric D'Hoker and published by American Mathematical Soc.. This book was released on 2002 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents contributions of participants of a workshop held at the Centre de Recherches Mathematiques (CRM), University of Montreal. It can be viewed as a sequel to Mirror Symmetry I (1998), Mirror Symmetry II (1996), and Mirror Symmetry III (1999), copublished by the AMS and International Press. The volume presents a broad survey of many of the noteworthy developments that have taken place in string theory, geometry, and duality since the mid 1990s. Some of the topics emphasized include the following: Integrable models and supersymmetric gauge theories; theory of M- and D-branes and noncommutative geometry; duality between strings and gauge theories; and elliptic genera and automorphic forms. Several introductory articles present an overview of the geometric and physical aspects of mirror symmetry and of corresponding developments in symplectic geometry. The book provides an efficient way for a very broad audience of mathematicians and physicists to explore the frontiers of research into this rapidly expanding area.

The Unity of Mathematics

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Publisher : Springer Science & Business Media
ISBN 13 : 0817644679
Total Pages : 632 pages
Book Rating : 4.8/5 (176 download)

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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 632 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

Toric Topology

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Publisher : American Mathematical Soc.
ISBN 13 : 147042214X
Total Pages : 518 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Toric Topology by : Victor M. Buchstaber

Download or read book Toric Topology written by Victor M. Buchstaber and published by American Mathematical Soc.. This book was released on 2015-07-15 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about toric topology, a new area of mathematics that emerged at the end of the 1990s on the border of equivariant topology, algebraic and symplectic geometry, combinatorics, and commutative algebra. It has quickly grown into a very active area with many links to other areas of mathematics, and continues to attract experts from different fields. The key players in toric topology are moment-angle manifolds, a class of manifolds with torus actions defined in combinatorial terms. Construction of moment-angle manifolds relates to combinatorial geometry and algebraic geometry of toric varieties via the notion of a quasitoric manifold. Discovery of remarkable geometric structures on moment-angle manifolds led to important connections with classical and modern areas of symplectic, Lagrangian, and non-Kaehler complex geometry. A related categorical construction of moment-angle complexes and polyhedral products provides for a universal framework for many fundamental constructions of homotopical topology. The study of polyhedral products is now evolving into a separate subject of homotopy theory. A new perspective on torus actions has also contributed to the development of classical areas of algebraic topology, such as complex cobordism. This book includes many open problems and is addressed to experts interested in new ideas linking all the subjects involved, as well as to graduate students and young researchers ready to enter this beautiful new area.