Categories for Quantum Theory, Heunen Chris

Автор: Matthew Ballard; Charles Doran; David Favero; Eric
Название: Superschool on Derived Categories and D-branes
ISBN: 3030062708 ISBN-13(EAN): 9783030062705
Издательство: Springer
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Цена: 18167.00 р.
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Описание: This book consists of a series of introductory lectures on mirror symmetry and its surrounding topics. These lectures were provided by participants in the PIMS Superschool for Derived Categories and D-branes in July 2016. Together, they form a comprehensive introduction to the field that integrates perspectives from mathematicians and physicists alike. These proceedings provide a pleasant and broad introduction into modern research topics surrounding string theory and mirror symmetry that is approachable to readers new to the subjects. These topics include constructions of various mirror pairs, approaches to mirror symmetry, connections to homological algebra, and physical motivations. Of particular interest is the connection between GLSMs, D-branes, birational geometry, and derived categories, which is explained both from a physical and mathematical perspective. The introductory lectures provided herein highlight many features of this emerging field and give concrete connections between the physics and the math.Mathematical readers will come away with a broader perspective on this field and a bit of physical intuition, while physicists will gain an introductory overview of the developing mathematical realization of physical predictions.

Автор: Ballard
Название: Superschool on Derived Categories and D-branes
ISBN: 3319916254 ISBN-13(EAN): 9783319916255
Издательство: Springer
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Цена: 25155.00 р.
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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: Simona Paoli
Название: Simplicial Methods for Higher Categories
ISBN: 3030056732 ISBN-13(EAN): 9783030056735
Издательство: Springer
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Цена: 19564.00 р.
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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: Denis-Charles Cisinski; Fr?d?ric D?glise
Название: Triangulated Categories of Mixed Motives
ISBN: 3030332411 ISBN-13(EAN): 9783030332419
Издательство: Springer
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Цена: 16769.00 р.
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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.