Perverse Sheaves And Applications To Representation Theory
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Perverse Sheaves And Applications To Representation Theory
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Author : Pramod N. Achar
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-09-27
Perverse Sheaves And Applications To Representation Theory written by Pramod N. Achar 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 2021-09-27 with Education categories.
Since its inception around 1980, the theory of perverse sheaves has been a vital tool of fundamental importance in geometric representation theory. This book, which aims to make this theory accessible to students and researchers, is divided into two parts. The first six chapters give a comprehensive account of constructible and perverse sheaves on complex algebraic varieties, including such topics as Artin's vanishing theorem, smooth descent, and the nearby cycles functor. This part of the book also has a chapter on the equivariant derived category, and brief surveys of side topics including étale and ℓ-adic sheaves, D-modules, and algebraic stacks. The last four chapters of the book show how to put this machinery to work in the context of selected topics in geometric representation theory: Kazhdan-Lusztig theory; Springer theory; the geometric Satake equivalence; and canonical bases for quantum groups. Recent developments such as the p-canonical basis are also discussed. The book has more than 250 exercises, many of which focus on explicit calculations with concrete examples. It also features a 4-page “Quick Reference” that summarizes the most commonly used facts for computations, similar to a table of integrals in a calculus textbook.
D Modules Perverse Sheaves And Representation Theory
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Author : Kiyoshi Takeuchi
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-12
D Modules Perverse Sheaves And Representation Theory written by Kiyoshi Takeuchi 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 2007-10-12 with Mathematics categories.
D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors' essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, representation theory.
Intersection Homology Perverse Sheaves
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Author : Laurenţiu G. Maxim
language : en
Publisher: Springer Nature
Release Date : 2019-11-30
Intersection Homology Perverse Sheaves written by Laurenţiu G. Maxim and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-30 with Mathematics categories.
This textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts throughout. By giving a taste of the main ideas in the field, the author welcomes new readers to this exciting area at the crossroads of topology, algebraic geometry, analysis, and differential equations. Those looking to delve further into the abstract theory will find ample references to facilitate navigation of both classic and recent literature. Beginning with an introduction to intersection homology from a geometric and topological viewpoint, the text goes on to develop the sheaf-theoretical perspective. Then algebraic geometry comes to the fore: a brief discussion of constructibility opens onto an in-depth exploration of perverse sheaves. Highlights from the following chapters include a detailed account of the proof of the Beilinson–Bernstein–Deligne–Gabber (BBDG) decomposition theorem, applications of perverse sheaves to hypersurface singularities, and a discussion of Hodge-theoretic aspects of intersection homology via Saito’s deep theory of mixed Hodge modules. An epilogue offers a succinct summary of the literature surrounding some recent applications. Intersection Homology & Perverse Sheaves is suitable for graduate students with a basic background in topology and algebraic geometry. By building context and familiarity with examples, the text offers an ideal starting point for those entering the field. This classroom-tested approach opens the door to further study and to current research.
Representations Of Finite Dimensional Algebras And Related Topics In Lie Theory And Geometry
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Author : Vlastimil Dlab
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Representations Of Finite Dimensional Algebras And Related Topics In Lie Theory And Geometry written by Vlastimil Dlab 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 2004 with Mathematics categories.
These proceedings are from the Tenth International Conference on Representations of Algebras and Related Topics (ICRA X) held at The Fields Institute. In addition to the traditional ``instructional'' workshop preceding the conference, there were also workshops on ``Commutative Algebra, Algebraic Geometry and Representation Theory'', ``Finite Dimensional Algebras, Algebraic Groups and Lie Theory'', and ``Quantum Groups and Hall Algebras''. These workshops reflect the latest developments and the increasing interest in areas that are closely related to the representation theory of finite dimensional associative algebras. Although these workshops were organized separately, their topics are strongly interrelated. The workshop on Commutative Algebra, Algebraic Geometry and Representation Theory surveyed various recently established connections, such as those pertaining to the classification of vector bundles or Cohen-Macaulay modules over Noetherian rings, coherent sheaves on curves, or ideals in Weyl algebras. In addition, methods from algebraic geometry or commutative algebra relating to quiver representations and varieties of modules were presented. The workshop on Finite Dimensional Algebras, Algebraic Groups and Lie Theory surveyed developments in finite dimensional algebras and infinite dimensional Lie theory, especially as the two areas interact and may have future interactions. The workshop on Quantum Groups and Hall Algebras dealt with the different approaches of using the representation theory of quivers (and species) in order to construct quantum groups, working either over finite fields or over the complex numbers. In particular, these proceedings contain a quite detailed outline of the use of perverse sheaves in order to obtain canonical bases. The book is recommended for graduate students and researchers in algebra and geometry.
Representation Theories And Algebraic Geometry
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Author : A. Broer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Representation Theories And Algebraic Geometry written by A. Broer 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 2013-03-09 with Mathematics categories.
The 12 lectures presented in Representation Theories and Algebraic Geometry focus on the very rich and powerful interplay between algebraic geometry and the representation theories of various modern mathematical structures, such as reductive groups, quantum groups, Hecke algebras, restricted Lie algebras, and their companions. This interplay has been extensively exploited during recent years, resulting in great progress in these representation theories. Conversely, a great stimulus has been given to the development of such geometric theories as D-modules, perverse sheafs and equivariant intersection cohomology. The range of topics covered is wide, from equivariant Chow groups, decomposition classes and Schubert varieties, multiplicity free actions, convolution algebras, standard monomial theory, and canonical bases, to annihilators of quantum Verma modules, modular representation theory of Lie algebras and combinatorics of representation categories of Harish-Chandra modules.
Algebraic And Diagrammatic Methods In Many Fermion Theory
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Author : Frank E. Harris
language : en
Publisher: Oxford University Press, USA
Release Date : 1992
Algebraic And Diagrammatic Methods In Many Fermion Theory written by Frank E. Harris and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Psychology categories.
The importance of electron correlation effects for the accurate description of the electronic structure of atoms, molecules and crystals is now widely recognized. In this text, modern theories of electronic structure and methods of incorporating electron correlation contributions are developed using a diagrammatic and algebraic formulation. This approach is intended to facilitate an understanding of the interconnections between the different approaches. As a further aid to understanding, the methods developed in the text are illustrated with examples from molecular and solid state quantum mechanics. The techniques presented here treat such topics as operator algebra, Hartree-perturbation theory and the coupled cluster method. The text is intended for graduate students in physical chemistry and physics.
Iwasawa Theory And Its Perspective Volume 2
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Author : Tadashi Ochiai
language : en
Publisher: American Mathematical Society
Release Date : 2024-04-25
Iwasawa Theory And Its Perspective Volume 2 written by Tadashi Ochiai and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-25 with Mathematics categories.
Iwasawa theory began in the late 1950s with a series of papers by Kenkichi Iwasawa on ideal class groups in the cyclotomic tower of number fields and their relation to $p$-adic $L$-functions. The theory was later generalized by putting it in the context of elliptic curves and modular forms. The main motivation for writing this book was the need for a total perspective of Iwasawa theory that includes the new trends of generalized Iwasawa theory. Another motivation is to update the classical theory for class groups, taking into account the changed point of view on Iwasawa theory. The goal of this second part of the three-part publication is to explain various aspects of the cyclotomic Iwasawa theory of $p$-adic Galois representations.
Intersection Homology Perverse Sheaves
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Author : Laurenţiu G. Maxim
language : en
Publisher: Springer
Release Date : 2020-12-12
Intersection Homology Perverse Sheaves written by Laurenţiu G. Maxim and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-12 with Mathematics categories.
This textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts throughout. By giving a taste of the main ideas in the field, the author welcomes new readers to this exciting area at the crossroads of topology, algebraic geometry, analysis, and differential equations. Those looking to delve further into the abstract theory will find ample references to facilitate navigation of both classic and recent literature. Beginning with an introduction to intersection homology from a geometric and topological viewpoint, the text goes on to develop the sheaf-theoretical perspective. Then algebraic geometry comes to the fore: a brief discussion of constructibility opens onto an in-depth exploration of perverse sheaves. Highlights from the following chapters include a detailed account of the proof of the Beilinson–Bernstein–Deligne–Gabber (BBDG) decomposition theorem, applications of perverse sheaves to hypersurface singularities, and a discussion of Hodge-theoretic aspects of intersection homology via Saito’s deep theory of mixed Hodge modules. An epilogue offers a succinct summary of the literature surrounding some recent applications. Intersection Homology & Perverse Sheaves is suitable for graduate students with a basic background in topology and algebraic geometry. By building context and familiarity with examples, the text offers an ideal starting point for those entering the field. This classroom-tested approach opens the door to further study and to current research.
Applications Of Group Theory To Combinatorics
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Author : Jack Koolen
language : en
Publisher: CRC Press
Release Date : 2008-07-02
Applications Of Group Theory To Combinatorics written by Jack Koolen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-02 with Mathematics categories.
Applications of Group Theory to Combinatorics contains 11 survey papers from international experts in combinatorics, group theory and combinatorial topology. The contributions cover topics from quite a diverse spectrum, such as design theory, Belyi functions, group theory, transitive graphs, regular maps, and Hurwitz problems, and present the state
Sheaves In Topology
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Author : Alexandru Dimca
language : en
Publisher:
Release Date : 2011-03-30
Sheaves In Topology written by Alexandru Dimca and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-30 with categories.