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Equivariant Sheaves And Functors
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Book Synopsis Equivariant Sheaves and Functors by : Joseph Bernstein
Download or read book Equivariant Sheaves and Functors written by Joseph Bernstein and published by Springer. This book was released on 2006-11-15 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: The equivariant derived category of sheaves is introduced. All usual functors on sheaves are extended to the equivariant situation. Some applications to the equivariant intersection cohomology are given. The theory may be useful to specialists in representation theory, algebraic geometry or topology.
Book Synopsis Equivariant Sheaves and Functors by : Joseph Bernstein
Download or read book Equivariant Sheaves and Functors written by Joseph Bernstein and published by . This book was released on 2014-01-15 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Extension Groups of Tautological Sheaves on Hilbert Schemes of Points on Surfaces by : Andreas Krug
Download or read book Extension Groups of Tautological Sheaves on Hilbert Schemes of Points on Surfaces written by Andreas Krug and published by Logos Verlag Berlin GmbH. This book was released on 2012 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis cohomological invariants of tensor products of tautological objects in the derived category of Hilbert schemes of points on surfaces are studied. The main tool is the Bridgeland-King-Reid-Haiman equivalence between the derived category of the Hilbert scheme and the equivariant derived category of the cartesian power of the surface. The work of Scala on this topic is further developed leading to a new description of the image of tensor products of tautological bundles under the BKRH equivalence. This description leads to formulas for the Euler characteristics of triple tensor products of tautological objects for arbitrary n and for arbitrary tensor products in the case n=2. Furthermore a formula for the extension groups between tautological objects is proven and the Yoneda product is described.
Book Synopsis Stable and Unstable Homotopy by : William G. Dwyer
Download or read book Stable and Unstable Homotopy written by William G. Dwyer and published by American Mathematical Soc.. This book was released on 1998-01-01 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of workshops on stable homotopy theory and on unstable homotopy theory held at The Fields Institute as part of the homotopy program during the year 1996. The papers in the volume describe current research in the subject, and all included works were refereed. Rather than being a summary of work to be published elsewhere, each paper is the unique source for the new material it contains. The book contains current research from international experts in the subject area, and presents open problems with directions for future research.
Book Synopsis Equivariant Analytic Localization of Group Representations by : Laura Ann Smithies
Download or read book Equivariant Analytic Localization of Group Representations written by Laura Ann Smithies and published by American Mathematical Soc.. This book was released on 2001 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of producing geometric constructions of the linear representations of a real connected semisimple Lie group with finite center, $G_0$, has been of great interest to representation theorists for many years now. A classical construction of this type is the Borel-Weil theorem, which exhibits each finite dimensional irreducible representation of $G_0$ as the space of global sections of a certain line bundle on the flag variety $X$ of the complexified Lie algebra $\mathfrak g$ of $G_0$.In 1990, Henryk Hecht and Joseph Taylor introduced a technique called analytic localization which vastly generalized the Borel-Weil theorem. Their method is similar in spirit to Beilinson and Bernstein's algebraic localization method, but it applies to $G_0$ representations themselves, instead of to their underlying Harish-Chandra modules. For technical reasons, the equivalence of categories implied by the analytic localization method is not as strong as it could be. In this paper, a refinement of the Hecht-Taylor method, called equivariant analytic localization, is developed. The technical advantages that equivariant analytic localization has over (non-equivariant) analytic localization are discussed and applications are indicated.
Author : Publisher :Springer Nature ISBN 13 :3031581202 Total Pages :729 pages Book Rating :4.0/5 (315 download)
Download or read book written by and published by Springer Nature. This book was released on with total page 729 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometry and Representation Theory of Real and p-adic groups by : Juan Tirao
Download or read book Geometry and Representation Theory of Real and p-adic groups written by Juan Tirao and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: The representation theory of Lie groups plays a central role in both clas sical and recent developments in many parts of mathematics and physics. In August, 1995, the Fifth Workshop on Representation Theory of Lie Groups and its Applications took place at the Universidad Nacional de Cordoba in Argentina. Organized by Joseph Wolf, Nolan Wallach, Roberto Miatello, Juan Tirao, and Jorge Vargas, the workshop offered expository courses on current research, and individual lectures on more specialized topics. The present vol ume reflects the dual character of the workshop. Many of the articles will be accessible to graduate students and others entering the field. Here is a rough outline of the mathematical content. (The editors beg the indulgence of the readers for any lapses in this preface in the high standards of historical and mathematical accuracy that were imposed on the authors of the articles. ) Connections between flag varieties and representation theory for real re ductive groups have been studied for almost fifty years, from the work of Gelfand and Naimark on principal series representations to that of Beilinson and Bernstein on localization. The article of Wolf provides a detailed introduc tion to the analytic side of these developments. He describes the construction of standard tempered representations in terms of square-integrable partially harmonic forms (on certain real group orbits on a flag variety), and outlines the ingredients in the Plancherel formula. Finally, he describes recent work on the complex geometry of real group orbits on partial flag varieties.
Book Synopsis Homotopy Methods in Algebraic Topology by : Nicholas Kuhn
Download or read book Homotopy Methods in Algebraic Topology written by Nicholas Kuhn and published by American Mathematical Soc.. This book was released on 2001-04-25 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings from the AMS-IMS-SIAM Summer Research Conference on Homotopy Methods in Algebraic Topology held at the University of Colorado (Boulder). The conference coincided with the sixtieth birthday of J. Peter May. An article is included reflecting his wide-ranging and influential contributions to the subject area. Other articles in the book discuss the ordinary, elliptic and real-oriented Adams spectral sequences, mapping class groups, configuration spaces, extended powers, operads, the telescope conjecture, $p$-compact groups, algebraic K theory, stable and unstable splittings, the calculus of functors, the $E_{\infty}$ tensor product, and equivariant cohomology theories. The book offers a compendious source on modern aspects of homotopy theoretic methods in many algebraic settings.
Book Synopsis Introductory Lectures on Equivariant Cohomology by : Loring W. Tu
Download or read book Introductory Lectures on Equivariant Cohomology written by Loring W. Tu and published by Princeton University Press. This book was released on 2020-03-03 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a clear introductory account of equivariant cohomology, a central topic in algebraic topology. Equivariant cohomology is concerned with the algebraic topology of spaces with a group action, or in other words, with symmetries of spaces. First defined in the 1950s, it has been introduced into K-theory and algebraic geometry, but it is in algebraic topology that the concepts are the most transparent and the proofs are the simplest. One of the most useful applications of equivariant cohomology is the equivariant localization theorem of Atiyah-Bott and Berline-Vergne, which converts the integral of an equivariant differential form into a finite sum over the fixed point set of the group action, providing a powerful tool for computing integrals over a manifold. Because integrals and symmetries are ubiquitous, equivariant cohomology has found applications in diverse areas of mathematics and physics. Assuming readers have taken one semester of manifold theory and a year of algebraic topology, Loring Tu begins with the topological construction of equivariant cohomology, then develops the theory for smooth manifolds with the aid of differential forms. To keep the exposition simple, the equivariant localization theorem is proven only for a circle action. An appendix gives a proof of the equivariant de Rham theorem, demonstrating that equivariant cohomology can be computed using equivariant differential forms. Examples and calculations illustrate new concepts. Exercises include hints or solutions, making this book suitable for self-study.
Book Synopsis Perverse Sheaves and Applications to Representation Theory by : Pramod N. Achar
Download or read book Perverse Sheaves and Applications to Representation Theory written by Pramod N. Achar and published by American Mathematical Soc.. This book was released on 2021-09-27 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Noncommutative Localization in Algebra and Topology by : Andrew Ranicki
Download or read book Noncommutative Localization in Algebra and Topology written by Andrew Ranicki and published by Cambridge University Press. This book was released on 2006-02-09 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative localization is a powerful algebraic technique for constructing new rings by inverting elements, matrices and more generally morphisms of modules. Originally conceived by algebraists (notably P. M. Cohn), it is now an important tool not only in pure algebra but also in the topology of non-simply-connected spaces, algebraic geometry and noncommutative geometry. This volume consists of 9 articles on noncommutative localization in algebra and topology by J. A. Beachy, P. M. Cohn, W. G. Dwyer, P. A. Linnell, A. Neeman, A. A. Ranicki, H. Reich, D. Sheiham and Z. Skoda. The articles include basic definitions, surveys, historical background and applications, as well as presenting new results. The book is an introduction to the subject, an account of the state of the art, and also provides many references for further material. It is suitable for graduate students and more advanced researchers in both algebra and topology.
Book Synopsis Algebraic Geometry: Hirzebruch 70 by : Friedrich Hirzebruch
Download or read book Algebraic Geometry: Hirzebruch 70 written by Friedrich Hirzebruch and published by American Mathematical Soc.. This book was released on 1999 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings from the conference on algebraic geometry in honor of Professor Friedrich Hirzebruch's 70th Birthday. The event was held at the Stefan Banach International Mathematical Center in Warsaw (Poland). Topics covered in the book include intersection theory, singularities, low-dimensional manifolds, moduli spaces, number theory, and interactions between mathematical physics and geometry. Also included are articles from notes of two special lectures. The first, by Professor M. Atiyah, describes the important contributions to the field of geometry by Professor Hirzebruch. The second article contains notes from the talk delivered at the conference by Professor Hirzebruch. Contributors to the volume are leading researchers in the field.
Book Synopsis Topology of Singular Spaces and Constructible Sheaves by : Jörg Schürmann
Download or read book Topology of Singular Spaces and Constructible Sheaves written by Jörg Schürmann and published by Birkhäuser. This book was released on 2012-12-06 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on the lecture notes of six courses delivered at a Cimpa Summer School in Temuco, Chile, in January 2001. Leading experts contribute with introductory articles covering a broad area in probability and its applications, such as mathematical physics and mathematics of finance. Written at graduate level, the lectures touch the latest advances on each subject, ranging from classical probability theory to modern developments. Thus the book will appeal to students, teachers and researchers working in probability theory or related fields.
Book Synopsis Integrability, Quantization, and Geometry: I. Integrable Systems by : Sergey Novikov
Download or read book Integrability, Quantization, and Geometry: I. Integrable Systems written by Sergey Novikov and published by American Mathematical Soc.. This book was released on 2021-04-12 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.
Book Synopsis Arithmetic L-Functions and Differential Geometric Methods by : Pierre Charollois
Download or read book Arithmetic L-Functions and Differential Geometric Methods written by Pierre Charollois and published by Springer Nature. This book was released on 2021-05-17 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an outgrowth of the conference “Regulators IV: An International Conference on Arithmetic L-functions and Differential Geometric Methods” that was held in Paris in May 2016. Gathering contributions by leading experts in the field ranging from original surveys to pure research articles, this volume provides comprehensive coverage of the front most developments in the field of regulator maps. Key topics covered are: • Additive polylogarithms • Analytic torsions • Chabauty-Kim theory • Local Grothendieck-Riemann-Roch theorems • Periods • Syntomic regulator The book contains contributions by M. Asakura, J. Balakrishnan, A. Besser, A. Best, F. Bianchi, O. Gregory, A. Langer, B. Lawrence, X. Ma, S. Müller, N. Otsubo, J. Raimbault, W. Raskin, D. Rössler, S. Shen, N. Triantafi llou, S. Ünver and J. Vonk.
Book Synopsis Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics by : CLAUDIO BARTOCCI
Download or read book Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics written by CLAUDIO BARTOCCI and published by Springer Science & Business Media. This book was released on 2009-06-12 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integral transforms, such as the Laplace and Fourier transforms, have been major tools in mathematics for at least two centuries. In the last three decades the development of a number of novel ideas in algebraic geometry, category theory, gauge theory, and string theory has been closely related to generalizations of integral transforms of a more geometric character. "Fourier–Mukai and Nahm Transforms in Geometry and Mathematical Physics" examines the algebro-geometric approach (Fourier–Mukai functors) as well as the differential-geometric constructions (Nahm). Also included is a considerable amount of material from existing literature which has not been systematically organized into a monograph. Key features: Basic constructions and definitions are presented in preliminary background chapters - Presentation explores applications and suggests several open questions - Extensive bibliography and index. This self-contained monograph provides an introduction to current research in geometry and mathematical physics and is intended for graduate students and researchers just entering this field.
Book Synopsis Categorification and Higher Representation Theory by : Anna Beliakova
Download or read book Categorification and Higher Representation Theory written by Anna Beliakova and published by American Mathematical Soc.. This book was released on 2017-02-21 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emergent mathematical philosophy of categorification is reshaping our view of modern mathematics by uncovering a hidden layer of structure in mathematics, revealing richer and more robust structures capable of describing more complex phenomena. Categorified representation theory, or higher representation theory, aims to understand a new level of structure present in representation theory. Rather than studying actions of algebras on vector spaces where algebra elements act by linear endomorphisms of the vector space, higher representation theory describes the structure present when algebras act on categories, with algebra elements acting by functors. The new level of structure in higher representation theory arises by studying the natural transformations between functors. This enhanced perspective brings into play a powerful new set of tools that deepens our understanding of traditional representation theory. This volume exhibits some of the current trends in higher representation theory and the diverse techniques that are being employed in this field with the aim of showcasing the many applications of higher representation theory. The companion volume (Contemporary Mathematics, Volume 684) is devoted to categorification in geometry, topology, and physics.
