Poincar Duality Algebras Macaulay S Dual Systems And Steenrod Operations
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Poincar Duality Algebras Macaulay S Dual Systems And Steenrod Operations
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Author : Dagmar M. Meyer
language : en
Publisher: Cambridge University Press
Release Date : 2005-08-18
Poincar Duality Algebras Macaulay S Dual Systems And Steenrod Operations written by Dagmar M. Meyer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-18 with Mathematics categories.
A monograph demonstrating remarkable and unexpected interdisciplinary connections in the areas of commutative algebra, invariant theory and algebraic topology.
Lefschetz Properties
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Author : Uwe Nagel
language : en
Publisher: Springer Nature
Release Date : 2024-08-30
Lefschetz Properties written by Uwe Nagel and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-30 with Mathematics categories.
The study of Lefschetz properties for Artinian algebras was motivated by the Lefschetz theory for projective manifolds. Recent developments have demonstrated important cases of the Lefschetz property beyond the original geometric settings, such as Coxeter groups or matroids. Furthermore, there are connections to other branches of mathematics, for example, commutative algebra, algebraic topology, and combinatorics. Important results in this area have been obtained by finding unexpected connections between apparently different topics. A conference in Cortona, Italy in September 2022 brought together researchers discussing recent developments and working on new problems related to the Lefschetz properties. The book will feature surveys on several aspects of the theory as well as articles on new results and open problems.
Quantum Stochastic Processes And Noncommutative Geometry
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Author : Kalyan B. Sinha
language : en
Publisher: Cambridge University Press
Release Date : 2007-01-25
Quantum Stochastic Processes And Noncommutative Geometry written by Kalyan B. Sinha and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-25 with Mathematics categories.
The classical theory of stochastic processes has important applications arising from the need to describe irreversible evolutions in classical mechanics; analogously quantum stochastic processes can be used to model the dynamics of irreversible quantum systems. Noncommutative, i.e. quantum, geometry provides a framework in which quantum stochastic structures can be explored. This book is the first to describe how these two mathematical constructions are related. In particular, key ideas of semigroups and complete positivity are combined to yield quantum dynamical semigroups (QDS). Sinha and Goswami also develop a general theory of Evans-Hudson dilation for both bounded and unbounded coefficients. The unique features of the book, including the interaction of QDS and quantum stochastic calculus with noncommutative geometry and a thorough discussion of this calculus with unbounded coefficients, will make it of interest to graduate students and researchers in functional analysis, probability and mathematical physics.
Convexity
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Author : Barry Simon
language : en
Publisher: Cambridge University Press
Release Date : 2011-05-19
Convexity written by Barry Simon and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-19 with Mathematics categories.
Convexity is important in theoretical aspects of mathematics and also for economists and physicists. In this monograph the author provides a comprehensive insight into convex sets and functions including the infinite-dimensional case and emphasizing the analytic point of view. Chapter one introduces the reader to the basic definitions and ideas that play central roles throughout the book. The rest of the book is divided into four parts: convexity and topology on infinite-dimensional spaces; Loewner's theorem; extreme points of convex sets and related issues, including the Krein–Milman theorem and Choquet theory; and a discussion of convexity and inequalities. The connections between disparate topics are clearly explained, giving the reader a thorough understanding of how convexity is useful as an analytic tool. A final chapter overviews the subject's history and explores further some of the themes mentioned earlier. This is an excellent resource for anyone interested in this central topic.
Jordan Structures In Geometry And Analysis
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Author : Cho-Ho Chu
language : en
Publisher: Cambridge University Press
Release Date : 2011-11-17
Jordan Structures In Geometry And Analysis written by Cho-Ho Chu and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-17 with Mathematics categories.
Jordan theory has developed rapidly in the last three decades, but very few books describe its diverse applications. Here, the author discusses some recent advances of Jordan theory in differential geometry, complex and functional analysis, with the aid of numerous examples and concise historical notes. These include: the connection between Jordan and Lie theory via the Tits–Kantor–Koecher construction of Lie algebras; a Jordan algebraic approach to infinite dimensional symmetric manifolds including Riemannian symmetric spaces; the one-to-one correspondence between bounded symmetric domains and JB*-triples; and applications of Jordan methods in complex function theory. The basic structures and some functional analytic properties of JB*-triples are also discussed. The book is a convenient reference for experts in complex geometry or functional analysis, as well as an introduction to these areas for beginning researchers. The recent applications of Jordan theory discussed in the book should also appeal to algebraists.
Rigidity In Higher Rank Abelian Group Actions Volume 1 Introduction And Cocycle Problem
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Author : Anatole Katok
language : en
Publisher: Cambridge University Press
Release Date : 2011-06-16
Rigidity In Higher Rank Abelian Group Actions Volume 1 Introduction And Cocycle Problem written by Anatole Katok and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-16 with Mathematics categories.
This self-contained monograph presents rigidity theory for a large class of dynamical systems, differentiable higher rank hyperbolic and partially hyperbolic actions. This first volume describes the subject in detail and develops the principal methods presently used in various aspects of the rigidity theory. Part I serves as an exposition and preparation, including a large collection of examples that are difficult to find in the existing literature. Part II focuses on cocycle rigidity, which serves as a model for rigidity phenomena as well as a useful tool for studying them. The book is an ideal reference for applied mathematicians and scientists working in dynamical systems and a useful introduction for graduate students interested in entering the field. Its wealth of examples also makes it excellent supplementary reading for any introductory course in dynamical systems.
Modern Approaches To The Invariant Subspace Problem
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Author : Isabelle Chalendar
language : en
Publisher: Cambridge University Press
Release Date : 2011-08-18
Modern Approaches To The Invariant Subspace Problem written by Isabelle Chalendar and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-18 with Mathematics categories.
One of the major unsolved problems in operator theory is the fifty-year-old invariant subspace problem, which asks whether every bounded linear operator on a Hilbert space has a nontrivial closed invariant subspace. This book presents some of the major results in the area, including many that were derived within the past few years and cannot be found in other books. Beginning with a preliminary chapter containing the necessary pure mathematical background, the authors present a variety of powerful techniques, including the use of the operator-valued Poisson kernel, various forms of the functional calculus, Hardy spaces, fixed point theorems, minimal vectors, universal operators and moment sequences. The subject is presented at a level accessible to postgraduate students, as well as established researchers. It will be of particular interest to those who study linear operators and also to those who work in other areas of pure mathematics.
Normal Approximations With Malliavin Calculus
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Author : Ivan Nourdin
language : en
Publisher: Cambridge University Press
Release Date : 2012-05-10
Normal Approximations With Malliavin Calculus written by Ivan Nourdin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-10 with Mathematics categories.
This book shows how quantitative central limit theorems can be deduced by combining two powerful probabilistic techniques: Stein's method and Malliavin calculus.
Nonlinear Perron Frobenius Theory
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Author : Bas Lemmens
language : en
Publisher: Cambridge University Press
Release Date : 2012-05-03
Nonlinear Perron Frobenius Theory written by Bas Lemmens and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-03 with Mathematics categories.
Guides the reader through the nonlinear Perron-Frobenius theory, introducing them to recent developments and challenging open problems.
Malliavin Calculus For L Vy Processes And Infinite Dimensional Brownian Motion
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Author : Horst Osswald
language : en
Publisher: Cambridge University Press
Release Date : 2012-03
Malliavin Calculus For L Vy Processes And Infinite Dimensional Brownian Motion written by Horst Osswald and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03 with Mathematics categories.
After functional, measure and stochastic analysis prerequisites, the author covers chaos decomposition, Skorohod integral processes, Malliavin derivative and Girsanov transformations.