Gauge Theory And Symplectic Geometry

Author : Jacques Hurtubise,François Lalonde
Publisher : Springer Science & Business Media
Page : 227 pages
File Size : 47,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401716673

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Gauge Theory and Symplectic Geometry by Jacques Hurtubise,François Lalonde Pdf

Gauge theory, symplectic geometry and symplectic topology are important areas at the crossroads of several mathematical disciplines. The present book, with expertly written surveys of recent developments in these areas, includes some of the first expository material of Seiberg-Witten theory, which has revolutionised the subjects since its introduction in late 1994. Topics covered include: introductions to Seiberg-Witten theory, to applications of the S-W theory to four-dimensional manifold topology, and to the classification of symplectic manifolds; an introduction to the theory of pseudo-holomorphic curves and to quantum cohomology; algebraically integrable Hamiltonian systems and moduli spaces; the stable topology of gauge theory, Morse-Floer theory; pseudo-convexity and its relations to symplectic geometry; generating functions; Frobenius manifolds and topological quantum field theory.

Author : S. K. Donaldson,C. B. Thomas
Publisher : Cambridge University Press
Page : 277 pages
File Size : 48,6 Mb
Release : 1990
Category : Mathematics
ISBN : 9780521399784

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Geometry of Low-Dimensional Manifolds: Volume 1, Gauge Theory and Algebraic Surfaces by S. K. Donaldson,C. B. Thomas Pdf

Distinguished researchers reveal the way different subjects (topology, differential and algebraic geometry and mathematical physics) interact in a text based on LMS Durham Symposium Lectures.

Author : Dietmar Salamon
Publisher : Unknown
Page : 244 pages
File Size : 47,5 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1107361923

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Symplectic Geometry by Dietmar Salamon Pdf

This volume is based on lectures given at a workshop and conference on symplectic geometry at the University of Warwick in August 1990. The area of symplectic geometry has developed rapidly in the past ten years with major new discoveries that were motivated by and have provided links with many other subjects such as dynamical systems, topology, gauge theory, mathematical physics and singularity theory. The conference brought together a number of leading experts in these areas of mathematics. The contributions to this volume reflect the richness of the subject and include expository papers as well as original research. They will be an essential source for all research mathematicians in symplectic geometry.

Author : Anastasios Mallios
Publisher : Springer Science & Business Media
Page : 293 pages
File Size : 41,9 Mb
Release : 2006-07-27
Category : Mathematics
ISBN : 9780817644741

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Modern Differential Geometry in Gauge Theories by Anastasios Mallios Pdf

This is original, well-written work of interest Presents for the first time (physical) field theories written in sheaf-theoretic language Contains a wealth of minutely detailed, rigorous computations, ususally absent from standard physical treatments Author's mastery of the subject and the rigorous treatment of this text make it invaluable

Author : Kenji Fukaya,Yong Geun Oh,K Ono,Gang Tian
Publisher : World Scientific
Page : 510 pages
File Size : 44,9 Mb
Release : 2001-11-19
Category : Mathematics
ISBN : 9789814490405

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Symplectic Geometry And Mirror Symmetry - Proceedings Of The 4th Kias Annual International Conference by Kenji Fukaya,Yong Geun Oh,K Ono,Gang Tian Pdf

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.

Author : Miguel Abreu,François Lalonde,Leonid Polterovich
Publisher : American Mathematical Soc.
Page : 355 pages
File Size : 52,9 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821870433

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New Perspectives and Challenges in Symplectic Field Theory by Miguel Abreu,François Lalonde,Leonid Polterovich Pdf

This volume, in honor of Yakov Eliashberg, gives a panorama of some of the most fascinating recent developments in symplectic, contact and gauge theories. It contains research papers aimed at experts, as well as a series of skillfully written surveys accessible for a broad geometrically oriented readership from the graduate level onwards. This collection will serve as an enduring source of information and ideas for those who want to enter this exciting area as well as for experts.

Author : Alexander Braverman,Michael Finkelberg,Andrei Negut,Alexei Oblomkov
Publisher : Springer Nature
Page : 137 pages
File Size : 54,7 Mb
Release : 2019-11-22
Category : Mathematics
ISBN : 9783030268565

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Geometric Representation Theory and Gauge Theory by Alexander Braverman,Michael Finkelberg,Andrei Negut,Alexei Oblomkov Pdf

This book offers a review of the vibrant areas of geometric representation theory and gauge theory, which are characterized by a merging of traditional techniques in representation theory with the use of powerful tools from algebraic geometry, and with strong inputs from physics. The notes are based on lectures delivered at the CIME school "Geometric Representation Theory and Gauge Theory" held in Cetraro, Italy, in June 2018. They comprise three contributions, due to Alexander Braverman and Michael Finkelberg, Andrei Negut, and Alexei Oblomkov, respectively. Braverman and Finkelberg’s notes review the mathematical theory of the Coulomb branch of 3D N=4 quantum gauge theories. The purpose of Negut’s notes is to study moduli spaces of sheaves on a surface, as well as Hecke correspondences between them. Oblomkov's notes concern matrix factorizations and knot homology. This book will appeal to both mathematicians and theoretical physicists and will be a source of inspiration for PhD students and researchers.

Author : Kenji Fukaya
Publisher : World Scientific
Page : 510 pages
File Size : 47,8 Mb
Release : 2001
Category : Mathematics
ISBN : 9789810247140

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Symplectic Geometry and Mirror Symmetry by Kenji Fukaya Pdf

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.

Author : Ana Cannas da Silva
Publisher : Springer
Page : 220 pages
File Size : 47,9 Mb
Release : 2004-10-27
Category : Mathematics
ISBN : 9783540453307

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Lectures on Symplectic Geometry by Ana Cannas da Silva Pdf

The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.

Author : Clay Mathematics Institute. Summer School
Publisher : American Mathematical Soc.
Page : 318 pages
File Size : 55,8 Mb
Release : 2006
Category : Mathematics
ISBN : 0821838458

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Floer Homology, Gauge Theory, and Low-Dimensional Topology by Clay Mathematics Institute. Summer School Pdf

Mathematical gauge theory studies connections on principal bundles, or, more precisely, the solution spaces of certain partial differential equations for such connections. Historically, these equations have come from mathematical physics, and play an important role in the description of the electro-weak and strong nuclear forces. The use of gauge theory as a tool for studying topological properties of four-manifolds was pioneered by the fundamental work of Simon Donaldson in theearly 1980s, and was revolutionized by the introduction of the Seiberg-Witten equations in the mid-1990s. Since the birth of the subject, it has retained its close connection with symplectic topology. The analogy between these two fields of study was further underscored by Andreas Floer's constructionof an infinite-dimensional variant of Morse theory that applies in two a priori different contexts: either to define symplectic invariants for pairs of Lagrangian submanifolds of a symplectic manifold, or to define topological This volume is based on lecture courses and advanced seminars given at the 2004 Clay Mathematics Institute Summer School at the Alfred Renyi Institute of Mathematics in Budapest, Hungary. Several of the authors have added a considerable amount of additional material tothat presented at the school, and the resulting volume provides a state-of-the-art introduction to current research, covering material from Heegaard Floer homology, contact geometry, smooth four-manifold topology, and symplectic four-manifolds. Information for our distributors: Titles in this seriesare copublished with the Clay Mathematics Institute (Cambridge, MA).

Author : Matilde Marcolli
Publisher : Springer
Page : 224 pages
File Size : 53,7 Mb
Release : 1999-12-15
Category : Mathematics
ISBN : 9789386279002

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Seiberg Witten Gauge Theory by Matilde Marcolli Pdf

Author : Hans U. Boden
Publisher : American Mathematical Soc.
Page : 362 pages
File Size : 43,5 Mb
Release : 2005
Category : Manifolds (Mathematics)
ISBN : 9780821837245

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Geometry and Topology of Manifolds by Hans U. Boden Pdf

This book contains expository papers that give an up-to-date account of recent developments and open problems in the geometry and topology of manifolds, along with several research articles that present new results appearing in published form for the first time. The unifying theme is the problem of understanding manifolds in low dimensions, notably in dimensions three and four, and the techniques include algebraic topology, surgery theory, Donaldson and Seiberg-Witten gauge theory,Heegaard Floer homology, contact and symplectic geometry, and Gromov-Witten invariants. The articles collected for this volume were contributed by participants of the Conference "Geometry and Topology of Manifolds" held at McMaster University on May 14-18, 2004 and are representative of the manyexcellent talks delivered at the conference.

Author : Robert Budzyński
Publisher : Unknown
Page : 412 pages
File Size : 51,5 Mb
Release : 1997
Category : Field theory (Physics)
ISBN : UOM:39015041351217

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Symplectic Singularities and Geometry of Gauge Fields by Robert Budzyński Pdf

Author : M. J. D. Hamilton,D. Kotschick
Publisher : Cambridge University Press
Page : 200 pages
File Size : 41,6 Mb
Release : 2023-12-21
Category : Mathematics
ISBN : 9781108905619

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Künneth Geometry by M. J. D. Hamilton,D. Kotschick Pdf

This clear and elegant text introduces Künneth, or bi-Lagrangian, geometry from the foundations up, beginning with a rapid introduction to symplectic geometry at a level suitable for undergraduate students. Unlike other books on this topic, it includes a systematic development of the foundations of Lagrangian foliations. The latter half of the text discusses Künneth geometry from the point of view of basic differential topology, featuring both new expositions of standard material and new material that has not previously appeared in book form. This subject, which has many interesting uses and applications in physics, is developed ab initio, without assuming any previous knowledge of pseudo-Riemannian or para-complex geometry. This book will serve both as a reference work for researchers, and as an invitation for graduate students to explore this field, with open problems included as inspiration for future research.

Author : Fabrizio Catanese,Denis Auroux,Gang Tian,Marco Manetti,Paul Seidel,Bernd Siebert,Ivan Smith
Publisher : Springer
Page : 363 pages
File Size : 55,7 Mb
Release : 2008-04-17
Category : Mathematics
ISBN : 9783540782797

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Symplectic 4-Manifolds and Algebraic Surfaces by Fabrizio Catanese,Denis Auroux,Gang Tian,Marco Manetti,Paul Seidel,Bernd Siebert,Ivan Smith Pdf

Modern approaches to the study of symplectic 4-manifolds and algebraic surfaces combine a wide range of techniques and sources of inspiration. Gauge theory, symplectic geometry, pseudoholomorphic curves, singularity theory, moduli spaces, braid groups, monodromy, in addition to classical topology and algebraic geometry, combine to make this one of the most vibrant and active areas of research in mathematics. It is our hope that the five lectures of the present volume given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2-10, 2003 will be useful to people working in related areas of mathematics and will become standard references on these topics. The volume is a coherent exposition of an active field of current research focusing on the introduction of new methods for the study of moduli spaces of complex structures on algebraic surfaces, and for the investigation of symplectic topology in dimension 4 and higher.