Vector Bundles And Representation Theory
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Vector Bundles And Representation Theory
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Author : Steven Dale Cutkosky
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Vector Bundles And Representation Theory written by Steven Dale Cutkosky 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 2003 with Mathematics categories.
This volume contains 13 papers from the conference on ``Hilbert Schemes, Vector Bundles and Their Interplay with Representation Theory''. The papers are written by leading mathematicians in algebraic geometry and representation theory and present the latest developments in the field. Among other contributions, the volume includes several very impressive and elegant theorems in representation theory by R. Friedman and J. W. Morgan, convolution on homology groups of moduli spaces of sheaves on K3 surfaces by H. Nakajima, and computation of the $S1$ fixed points in Quot-schemes and mirror principle computations for Grassmanians by S.-T. Yau, et al. The book is of interest to graduate students and researchers in algebraic geometry, representation theory, topology and their applications to high energy physics.
Basic Bundle Theory And K Cohomology Invariants
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Author : Dale Husemöller
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-18
Basic Bundle Theory And K Cohomology Invariants written by Dale Husemöller 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 2007-12-18 with Mathematics categories.
Based on several recent courses given to mathematical physics students, this volume is an introduction to bundle theory. It aims to provide newcomers to the field with solid foundations in topological K-theory. A fundamental theme, emphasized in the book, centers around the gluing of local bundle data related to bundles into a global object. One renewed motivation for studying this subject, comes from quantum field theory, where topological invariants play an important role.
Moduli Spaces And Vector Bundles
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Author : Steve Bradlow
language : en
Publisher: Cambridge University Press
Release Date : 2009-05-21
Moduli Spaces And Vector Bundles written by Steve Bradlow and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-21 with Mathematics categories.
Coverage includes foundational material as well as current research, authored by top specialists within their fields.
Cohomology Of Vector Bundles And Syzygies
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Author : Jerzy Weyman
language : en
Publisher: Cambridge University Press
Release Date : 2003-06-09
Cohomology Of Vector Bundles And Syzygies written by Jerzy Weyman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-09 with Mathematics categories.
The central theme of this book is an exposition of the geometric technique of calculating syzygies. It is written from a point of view of commutative algebra, and without assuming any knowledge of representation theory the calculation of syzygies of determinantal varieties is explained. The starting point is a definition of Schur functors, and these are discussed from both an algebraic and geometric point of view. Then a chapter on various versions of Bott's Theorem leads on to a careful explanation of the technique itself, based on a description of the direct image of a Koszul complex. Applications to determinantal varieties follow, plus there are also chapters on applications of the technique to rank varieties for symmetric and skew symmetric tensors of arbitrary degree, closures of conjugacy classes of nilpotent matrices, discriminants and resultants. Numerous exercises are included to give the reader insight into how to apply this important method.
Geometry Of Moduli Spaces And Representation Theory
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Author : Roman Bezrukavnikov
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-12-15
Geometry Of Moduli Spaces And Representation Theory written by Roman Bezrukavnikov 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 2017-12-15 with Mathematics categories.
This book is based on lectures given at the Graduate Summer School of the 2015 Park City Mathematics Institute program “Geometry of moduli spaces and representation theory”, and is devoted to several interrelated topics in algebraic geometry, topology of algebraic varieties, and representation theory. Geometric representation theory is a young but fast developing research area at the intersection of these subjects. An early profound achievement was the famous conjecture by Kazhdan–Lusztig about characters of highest weight modules over a complex semi-simple Lie algebra, and its subsequent proof by Beilinson-Bernstein and Brylinski-Kashiwara. Two remarkable features of this proof have inspired much of subsequent development: intricate algebraic data turned out to be encoded in topological invariants of singular geometric spaces, while proving this fact required deep general theorems from algebraic geometry. Another focus of the program was enumerative algebraic geometry. Recent progress showed the role of Lie theoretic structures in problems such as calculation of quantum cohomology, K-theory, etc. Although the motivation and technical background of these constructions is quite different from that of geometric Langlands duality, both theories deal with topological invariants of moduli spaces of maps from a target of complex dimension one. Thus they are at least heuristically related, while several recent works indicate possible strong technical connections. The main goal of this collection of notes is to provide young researchers and experts alike with an introduction to these areas of active research and promote interaction between the two related directions.
The Topology Of Fibre Bundles
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Author : Norman Earl Steenrod
language : en
Publisher:
Release Date : 1951
The Topology Of Fibre Bundles written by Norman Earl Steenrod and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1951 with Mathematics categories.
Fibre bundles, now an integral part of differential geometry, are also of great importance in modern physics--such as in gauge theory. This book, a succinct introduction to the subject by renown mathematician Norman Steenrod, was the first to present the subject systematically. It begins with a general introduction to bundles, including such topics as differentiable manifolds and covering spaces. The author then provides brief surveys of advanced topics, such as homotopy theory and cohomology theory, before using them to study further properties of fibre bundles. The result is a classic and timeless work of great utility that will appeal to serious mathematicians and theoretical physicists alike.
Representation Theory And Algebraic Geometry
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Author : A. Martsinkovsky
language : en
Publisher: Cambridge University Press
Release Date : 1997-05-15
Representation Theory And Algebraic Geometry written by A. Martsinkovsky and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-05-15 with Mathematics categories.
For any researcher working in representation theory, algebraic or arithmetic geometry.
Basics Of Representation Theory
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Author : Udayan Bhattacharya
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Basics Of Representation Theory written by Udayan Bhattacharya and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
Delve into the captivating world of "Basics of Representation Theory," a comprehensive guide designed for students, researchers, and enthusiasts eager to explore the intricate symmetries and structures that underpin modern mathematics. Our book offers a detailed introduction to foundational concepts, providing a solid understanding of group actions, linear representations, and character theory. From there, it explores the algebraic structures of irreducible representations, breaking down the decomposition into irreducible components and examining the properties of characters. Readers will journey through diverse topics, including the representation theory of symmetric groups, Lie groups, and algebraic groups, as well as advanced topics such as the representation theory of finite groups, the Langlands program, and applications in quantum mechanics and number theory. With a wealth of examples, illustrations, and exercises, "Basics of Representation Theory" ensures a hands-on approach to learning, encouraging practical exploration and problem-solving. The book also includes numerous references and further reading suggestions for those who wish to delve deeper into specific topics. Written in a clear and accessible style, this book caters to all levels, from undergraduate students encountering representation theory for the first time to experienced researchers seeking fresh insights. With its comprehensive coverage and diverse applications, "Basics of Representation Theory" is an invaluable resource for anyone interested in the beauty and depth of this field.
Topology And Representation Theory
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Author : Eric M. Friedlander
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Topology And Representation Theory written by Eric M. Friedlander 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 1994 with Mathematics categories.
During 1991-1992, Northwestern University conducted a special emphasis year on the topic, "The connections between topology and representation theory." Activities over the year culminated in a conference in May 1992 which attracted over 120 participants. Most of the plenary lectures at the conference were expository and designed to introduce current trends to graduate students and nonspecialists familiar with algebraic topology. This volume contains refereed papers presented or solicited at the conference; one paper is based on a seminar given during the emphasis year.
Transformation Groups And Representation Theory
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Author : T. Tom Dieck
language : en
Publisher: Lecture Notes in Mathematics
Release Date : 1979-11
Transformation Groups And Representation Theory written by T. Tom Dieck and has been published by Lecture Notes in Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979-11 with Mathematics categories.