Superschool on Derived Categories and D-branes, Matthew Ballard; Charles Doran; David Favero; Eric
Автор: Masaki Kashiwara, Pierre Schapira Название: Categories and Sheaves ISBN: 3642066208 ISBN-13(EAN): 9783642066207 Издательство: Springer Рейтинг: Цена: 67070.00 T Наличие на складе: Есть Описание:
Categories and sheaves, which emerged in the middle of the last century as an enrichment for the concepts of sets and functions, appear almost everywhere in mathematics nowadays.
This book covers categories, homological algebra and sheaves in a systematic and exhaustive manner starting from scratch, and continues with full proofs to an exposition of the most recent results in the literature, and sometimes beyond.
The authors present the general theory of categories and functors, emphasising inductive and projective limits, tensor categories, representable functors, ind-objects and localization. Then they study homological algebra including additive, abelian, triangulated categories and also unbounded derived categories using transfinite induction and accessible objects. Finally, sheaf theory as well as twisted sheaves and stacks appear in the framework of Grothendieck topologies.
Автор: Reiner Hermann Название: Monoidal Categories and the Gerstenhaber Bracket in Hochschild Cohomology ISBN: 1470419955 ISBN-13(EAN): 9781470419950 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 85930.00 T Наличие на складе: Невозможна поставка. Описание: "Volume 243, number 1151 (fourth of 4 numbers), September 2016."
Автор: Denis-Charles Cisinski Название: Higher Categories and Homotopical Algebra ISBN: 1108473202 ISBN-13(EAN): 9781108473200 Издательство: Cambridge Academ Рейтинг: Цена: 67590.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This user-friendly book introduces modern homotopy theory through the lens of higher categories after Joyal and Lurie. Starting from scratch it guides graduate students and researchers through the powerful tools that the theory provides for applications in such areas as algebraic geometry, representation theory, algebra and logic.
Автор: Alberto Facchini, Lorna Gregory, Sonia L`Innocente, Marcus Tressl Название: Model Theory of Modules, Algebras and Categories ISBN: 1470443678 ISBN-13(EAN): 9781470443672 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 108680.00 T Наличие на складе: Нет в наличии. Описание: This volume contains the proceedings of the international conference Model Theory of Modules, Algebras and Categories, held from July 28-August 2, 2017, at the Ettore Majorana Foundation and Centre for Scientific Culture in Erice, Italy.Papers contained in this volume cover recent developments in model theory, module theory and category theory, and their intersection.
Автор: C.T. Dodson Название: Categories, Bundles and Spacetime Topology ISBN: 9027727716 ISBN-13(EAN): 9789027727718 Издательство: Springer Рейтинг: Цена: 88500.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Gad in Crane Feathers' in R. Brown'The point of a Pin'. van Gulik's TheChinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging SUbdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Автор: Pavel Etingof, Shlomo Gelaki, Dmitri Nikshych, Victor Ostrik Название: Tensor Categories ISBN: 1470434415 ISBN-13(EAN): 9781470434410 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 64680.00 T Наличие на складе: Невозможна поставка. Описание: Is there a vector space whose dimension is the golden ratio? Of course not-the golden ratio is not an integer! But this can happen for generalizations of vector spaces-objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.
Автор: Simona Paoli Название: Simplicial Methods for Higher Categories ISBN: 3030056732 ISBN-13(EAN): 9783030056735 Издательство: Springer Рейтинг: Цена: 130430.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This monograph presents a new model of mathematical structures called weak n-categories. These structures find their motivation in a wide range of fields, from algebraic topology to mathematical physics, algebraic geometry and mathematical logic.While strict n-categories are easily defined in terms associative and unital composition operations they are of limited use in applications, which often call for weakened variants of these laws. The author proposes a new approach to this weakening, whose generality arises not from a weakening of such laws but from the very geometric structure of its cells; a geometry dubbed weak globularity. The new model, called weakly globular n-fold categories, is one of the simplest known algebraic structures yielding a model of weak n-categories. The central result is the equivalence of this model to one of the existing models, due to Tamsamani and further studied by Simpson. This theory has intended applications to homotopy theory, mathematical physics and to long-standing open questions in category theory.As the theory is described in elementary terms and the book is largely self-contained, it is accessible to beginning graduate students and to mathematicians from a wide range of disciplines well beyond higher category theory. The new model makes a transparent connection between higher category theory and homotopy theory, rendering it particularly suitable for category theorists and algebraic topologists. Although the results are complex, readers are guided with an intuitive explanation before each concept is introduced, and with diagrams showing the interconnections between the main ideas and results.
Автор: Ballard Название: Superschool on Derived Categories and D-branes ISBN: 3319916254 ISBN-13(EAN): 9783319916255 Издательство: Springer Рейтинг: Цена: 167700.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Abelian and Triangulated Categories (C. Hanratty).- Derived Categories and Derived Functors (N.K. Chidambaram).- Introduction to Quivers (M. Chinen).- Semi-orthogonal Decompositions of Derived Categories (Y. Liu).- Introduction to Bridgeland Stability Conditions (R. Tramel).- A Brief Introduction to Geometric Invariant Theory (N. Grieve).- Birational Geometry and Derived Categories (C. Diemer).- Introduction to Mirror Symmetry (R. Hughes).- Batyrev Mirror Symmetry (M. Talpo).- Differential Graded Categories (A.A. Takeda).- Introduction to Symplectic Geometry and Fukaya Category (A.Z. Zhang).- Homological Mirror Symmetry (A. Harder).- The Syz Conjecture Via Homological Mirror Symmetry (D. Bejleri).- The Derived Category of Coherent Sheaves and B-model Topological String Theory (S. Pietromonaco).- Introduction to Topological String Theories (K. Osuga).- An Overview of B-branes in Gauged Linear Sigma Models (N. Ishtiaque).
Автор: Heunen Chris Название: Categories for Quantum Theory ISBN: 0198739613 ISBN-13(EAN): 9780198739616 Издательство: Oxford Academ Рейтинг: Цена: 51730.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Categories for Quantum Theory: An Introduction lays foundations for an approach to quantum theory that uses category theory, a branch of pure mathematics. Prior knowledge of quantum information theory or category theory helps, but is not assumed, and basic linear algebra and group theory suffices.
Автор: Denis-Charles Cisinski; Fr?d?ric D?glise Название: Triangulated Categories of Mixed Motives ISBN: 3030332411 ISBN-13(EAN): 9783030332419 Издательство: Springer Рейтинг: Цена: 111790.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The primary aim of this monograph is to achieve part of Beilinson`s program on mixed motives using Voevodsky`s theories of A1-homotopy and motivic complexes.
Автор: Tony Pantev, Carlos Simpson, Bertrand Toen, Michel Vaquie, Gabriele Vezzosi Название: Stacks and Categories in Geometry, Topology, and Algebra ISBN: 1470415577 ISBN-13(EAN): 9781470415570 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 104410.00 T Наличие на складе: Невозможна поставка. Описание: This volume contains the proceedings of the CATS4 Conference on Higher Categorical Structures and their Interactions with Algebraic Geometry, Algebraic Topology and Algebra, held from July 2-7, 2012, at CIRM in Luminy, France.Over the past several years, the CATS conference series has brought together top level researchers from around the world interested in relative and higher category theory and its applications to classical mathematical domains.Included in this volume is a collection of articles covering the applications of categories and stacks to geometry, topology and algebra. Techniques such as localization, model categories, simplicial objects, sheaves of categories, mapping stacks, dg structures, hereditary categories, and derived stacks, are applied to give new insight on cluster algebra, Lagrangians, trace theories, loop spaces, structured surfaces, stability, ind-coherent complexes and 1-affineness showing up in geometric Langlands, branching out to many related topics along the way.
Автор: Nicolas Andruskiewitsch, Dmitri Nikshych Название: Tensor Categories and Hopf Algebras ISBN: 147044321X ISBN-13(EAN): 9781470443214 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 108680.00 T Наличие на складе: Нет в наличии. Описание: This volume contains the proceedings of the scientific session ``Hopf Algebras and Tensor Categories'', held from July 27-28, 2017, at the Mathematical Congress of the Americas in Montreal, Canada.Papers highlight the latest advances and research directions in the theory of tensor categories and Hopf algebras. Primary topics include classification and structure theory of tensor categories and Hopf algebras, Gelfand-Kirillov dimension theory for Nichols algebras, module categories and weak Hopf algebras, Hopf Galois extensions, graded simple algebras, and bialgebra coverings.
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