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Wigner Type Theorems For Hilbert Grassmannians
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Book Synopsis Wigner-Type Theorems for Hilbert Grassmannians by : Mark Pankov
Download or read book Wigner-Type Theorems for Hilbert Grassmannians written by Mark Pankov and published by Cambridge University Press. This book was released on 2020-01-16 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to the geometric approach to Wigner's theorem and its role in quantum mechanics.
Book Synopsis Wigner-Type Theorems for Hilbert Grassmannians by : Mark Pankov
Download or read book Wigner-Type Theorems for Hilbert Grassmannians written by Mark Pankov and published by Cambridge University Press. This book was released on 2020-01-16 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wigner's theorem is a fundamental part of the mathematical formulation of quantum mechanics. The theorem characterizes unitary and anti-unitary operators as symmetries of quantum mechanical systems, and is a key result when relating preserver problems to quantum mechanics. At the heart of this book is a geometric approach to Wigner-type theorems, unifying both classical and more recent results. Readers are initiated in a wide range of topics from geometric transformations of Grassmannians to lattices of closed subspaces, before moving on to a discussion of applications. An introduction to all the key aspects of the basic theory is included as are plenty of examples, making this book a useful resource for beginning graduate students and non-experts, as well as a helpful reference for specialist researchers.
Book Synopsis Modern Trends in Algebra and Representation Theory by : David Jordan
Download or read book Modern Trends in Algebra and Representation Theory written by David Jordan and published by Cambridge University Press. This book was released on 2023-08-17 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expanding upon the material delivered during the LMS Autumn Algebra School 2020, this volume reflects the fruitful connections between different aspects of representation theory. Each survey article addresses a specific subject from a modern angle, beginning with an exploration of the representation theory of associative algebras, followed by the coverage of important developments in Lie theory in the past two decades, before the final sections introduce the reader to three strikingly different aspects of group theory. Written at a level suitable for graduate students and researchers in related fields, this book provides pure mathematicians with a springboard into the vast and growing literature in each area.
Book Synopsis An Indefinite Excursion in Operator Theory by : Aurelian Gheondea
Download or read book An Indefinite Excursion in Operator Theory written by Aurelian Gheondea and published by Cambridge University Press. This book was released on 2022-07-28 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a modern, readable introduction to spaces with indefinite inner product and their operator theory.
Book Synopsis Maurer–Cartan Methods in Deformation Theory by : Vladimir Dotsenko
Download or read book Maurer–Cartan Methods in Deformation Theory written by Vladimir Dotsenko and published by Cambridge University Press. This book was released on 2023-08-31 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering an exceptional range of topics, this text provides a unique overview of the Maurer-Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a new conceptual treatment of the twisting procedure, guiding the reader through various versions with the help of plentiful motivating examples for graduate students as well as researchers. Topics covered include a novel approach to the twisting procedure for operads leading to Kontsevich graph homology and a description of the twisting procedure for (homotopy) associative algebras or (homotopy) Lie algebras using the biggest deformation gauge group ever considered. The book concludes with concise surveys of recent applications in areas including higher category theory and deformation theory.
Book Synopsis The Logical Approach to Automatic Sequences by : Jeffrey Shallit
Download or read book The Logical Approach to Automatic Sequences written by Jeffrey Shallit and published by Cambridge University Press. This book was released on 2022-09-30 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Automatic sequences are sequences over a finite alphabet generated by a finite-state machine. This book presents a novel viewpoint on automatic sequences, and more generally on combinatorics on words, by introducing a decision method through which many new results in combinatorics and number theory can be automatically proved or disproved with little or no human intervention. This approach to proving theorems is extremely powerful, allowing long and error-prone case-based arguments to be replaced by simple computations. Readers will learn how to phrase their desired results in first-order logic, using free software to automate the computation process. Results that normally require multipage proofs can emerge in milliseconds, allowing users to engage with mathematical questions that would otherwise be difficult to solve. With more than 150 exercises included, this text is an ideal resource for researchers, graduate students, and advanced undergraduates studying combinatorics, sequences, and number theory.
Book Synopsis Bounded Cohomology and Simplicial Volume by : Caterina Campagnolo
Download or read book Bounded Cohomology and Simplicial Volume written by Caterina Campagnolo and published by Cambridge University Press. This book was released on 2022-11-30 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: An overview of bounded cohomology and simplicial volume covering the basics of the subject and recent research directions.
Book Synopsis Algebraic Combinatorics and the Monster Group by : Alexander A. Ivanov
Download or read book Algebraic Combinatorics and the Monster Group written by Alexander A. Ivanov and published by Cambridge University Press. This book was released on 2023-08-17 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering, arguably, one of the most attractive and mysterious mathematical objects, the Monster group, this text strives to provide an insightful introduction and the discusses the current state of the field. The Monster group is related to many areas of mathematics, as well as physics, from number theory to string theory. This book cuts through the complex nature of the field, highlighting some of the mysteries and intricate relationships involved. Containing many meaningful examples and a manual introduction to the computer package GAP, it provides the opportunity and resources for readers to start their own calculations. Some 20 experts here share their expertise spanning this exciting field, and the resulting volume is ideal for researchers and graduate students working in Combinatorial Algebra, Group theory and related areas.
Book Synopsis Surveys in Combinatorics 2024 by : Felix Fischer
Download or read book Surveys in Combinatorics 2024 written by Felix Fischer and published by Cambridge University Press. This book was released on 2024-06-13 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains surveys of current research directions in combinatorics written by leading researchers in their fields.
Book Synopsis C∞-Algebraic Geometry with Corners by : Kelli Francis-Staite
Download or read book C∞-Algebraic Geometry with Corners written by Kelli Francis-Staite and published by Cambridge University Press. This book was released on 2023-12-31 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Schemes in algebraic geometry can have singular points, whereas differential geometers typically focus on manifolds which are nonsingular. However, there is a class of schemes, 'C∞-schemes', which allow differential geometers to study a huge range of singular spaces, including 'infinitesimals' and infinite-dimensional spaces. These are applied in synthetic differential geometry, and derived differential geometry, the study of 'derived manifolds'. Differential geometers also study manifolds with corners. The cube is a 3-dimensional manifold with corners, with boundary the six square faces. This book introduces 'C∞-schemes with corners', singular spaces in differential geometry with good notions of boundary and corners. They can be used to define 'derived manifolds with corners' and 'derived orbifolds with corners'. These have applications to major areas of symplectic geometry involving moduli spaces of J-holomorphic curves. This work will be a welcome source of information and inspiration for graduate students and researchers working in differential or algebraic geometry.
Book Synopsis Discrete Quantum Walks on Graphs and Digraphs by : Chris Godsil
Download or read book Discrete Quantum Walks on Graphs and Digraphs written by Chris Godsil and published by Cambridge University Press. This book was released on 2022-12-31 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explore the mathematics arising from discrete quantum walks in this introduction to a rapidly developing area.
Book Synopsis Elliptic Regularity Theory by Approximation Methods by : Edgard A. Pimentel
Download or read book Elliptic Regularity Theory by Approximation Methods written by Edgard A. Pimentel and published by Cambridge University Press. This book was released on 2022-06-30 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting the basics of elliptic PDEs in connection with regularity theory, the book bridges fundamental breakthroughs – such as the Krylov–Safonov and Evans–Krylov results, Caffarelli's regularity theory, and the counterexamples due to Nadirashvili and Vlăduţ – and modern developments, including improved regularity for flat solutions and the partial regularity result. After presenting this general panorama, accounting for the subtleties surrounding C-viscosity and Lp-viscosity solutions, the book examines important models through approximation methods. The analysis continues with the asymptotic approach, based on the recession operator. After that, approximation techniques produce a regularity theory for the Isaacs equation, in Sobolev and Hölder spaces. Although the Isaacs operator lacks convexity, approximation methods are capable of producing Hölder continuity for the Hessian of the solutions by connecting the problem with a Bellman equation. To complete the book, degenerate models are studied and their optimal regularity is described.
Book Synopsis Invariance of Modules under Automorphisms of their Envelopes and Covers by : Ashish K. Srivastava
Download or read book Invariance of Modules under Automorphisms of their Envelopes and Covers written by Ashish K. Srivastava and published by Cambridge University Press. This book was released on 2021-03-18 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of invariance of modules under automorphisms of their envelopes and covers has opened up a whole new direction in the study of module theory. It offers a new perspective on generalizations of injective, pure-injective and flat-cotorsion modules beyond relaxing conditions on liftings of homomorphisms. This has set off a flurry of work in the area, with hundreds of papers using the theory appearing in the last decade. This book gives the first unified treatment of the topic. The authors are real experts in the area, having played a major part in the breakthrough of this new theory and its subsequent applications. The first chapter introduces the basics of ring and module theory needed for the following sections, making it self-contained and suitable for graduate students. The authors go on to develop and explain their tools, enabling researchers to employ them, extend and simplify known results in the literature and to solve longstanding problems in module theory, many of which are discussed at the end of the book.
Book Synopsis Stacks Project Expository Collection by : Pieter Belmans
Download or read book Stacks Project Expository Collection written by Pieter Belmans and published by Cambridge University Press. This book was released on 2022-09-30 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Stacks Project Expository Collection (SPEC) compiles expository articles in advanced algebraic geometry, intended to bring graduate students and researchers up to speed on recent developments in the geometry of algebraic spaces and algebraic stacks. The articles in the text make explicit in modern language many results, proofs, and examples that were previously only implicit, incomplete, or expressed in classical terms in the literature. Where applicable this is done by explicitly referring to the Stacks project for preliminary results. Topics include the construction and properties of important moduli problems in algebraic geometry (such as the Deligne–Mumford compactification of the moduli of curves, the Picard functor, or moduli of semistable vector bundles and sheaves), and arithmetic questions for fields and algebraic spaces.
Book Synopsis Lectures on Orthogonal Polynomials and Special Functions by : Howard S. Cohl
Download or read book Lectures on Orthogonal Polynomials and Special Functions written by Howard S. Cohl and published by Cambridge University Press. This book was released on 2020-10-15 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by experts in their respective fields, this collection of pedagogic surveys provides detailed insight and background into five separate areas at the forefront of modern research in orthogonal polynomials and special functions at a level suited to graduate students. A broad range of topics are introduced including exceptional orthogonal polynomials, q-series, applications of spectral theory to special functions, elliptic hypergeometric functions, and combinatorics of orthogonal polynomials. Exercises, examples and some open problems are provided. The volume is derived from lectures presented at the OPSF-S6 Summer School at the University of Maryland, and has been carefully edited to provide a coherent and consistent entry point for graduate students and newcomers.
Book Synopsis Differential Geometry in the Large by : Owen Dearricott
Download or read book Differential Geometry in the Large written by Owen Dearricott and published by Cambridge University Press. This book was released on 2020-10-22 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: From Ricci flow to GIT, physics to curvature bounds, Sasaki geometry to almost formality. This is differential geometry at large.
Book Synopsis Surveys in Combinatorics 2022 by : Anthony Nixon
Download or read book Surveys in Combinatorics 2022 written by Anthony Nixon and published by Cambridge University Press. This book was released on 2022-06-09 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains surveys of current research directions in combinatorics written by leading researchers in their fields.
