new mathematical monographs - 三民網路書店

1.

K-stability of Fano Varieties

作者：Chenyang (Princeton University Xu New Jersey) 出版社：Cambridge University Press 出版日：2025/04/30 裝訂：精裝

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2.

Abstract Chiral Polytopes

作者：Daniel Pellicer (Universidad Nacional Autonoma de Mexico) 出版社：Cambridge University Press 出版日：2025/04/30 裝訂：精裝

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3.

Homotopy Theory of Higher Categories

作者：Carlos Simpson 出版社：Cambridge Univ Pr 出版日：2011/11/30 裝訂：精裝

The study of higher categories is attracting growing interest for its many applications in topology, algebraic geometry, mathematical physics and category theory. In this highly readable book, Carlos Simpson develops a full set of homotopical algebra techniques and proposes a working theory of higher categories. Starting with a cohesive overview of the many different approaches currently used by researchers, the author proceeds with a detailed exposition of one of the most widely used techniques: the construction of a Cartesian Quillen model structure for higher categories. The fully iterative construction applies to enrichment over any Cartesian model category, and yields model categories for weakly associative n-categories and Segal n-categories. A corollary is the construction of higher functor categories which fit together to form the (n+1)-category of n-categories. The approach uses Tamsamani's definition based on Segal's ideas, iterated as in Pelissier's thesis using modern

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4.

Entropy in Dynamical Systems

作者：Tomasz Downarowicz 出版社：Cambridge Univ Pr 出版日：2011/06/20 裝訂：精裝

This comprehensive text on entropy covers three major types of dynamics: measure preserving transformations; continuous maps on compact spaces; and operators on function spaces. Part I contains proofs of the Shannon–McMillan–Breiman Theorem, the Ornstein–Weiss Return Time Theorem, the Krieger Generator Theorem and, among the newest developments, the ergodic law of series. In Part II, after an expanded exposition of classical topological entropy, the book addresses symbolic extension entropy. It offers deep insight into the theory of entropy structure and explains the role of zero-dimensional dynamics as a bridge between measurable and topological dynamics. Part III explains how both measure-theoretic and topological entropy can be extended to operators on relevant function spaces. Intuitive explanations, examples, exercises and open problems make this an ideal text for a graduate course on entropy theory. More experienced researchers can also find inspiration for further research.

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5.

Factorization Algebras in Quantum Field Theory

作者：Kevin Costello; Owen (University of Massachusetts Gwilliam Amherst) 出版社：Cambridge University Press 出版日：2021/11/30 裝訂：平裝

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6.

Discriminant Equations in Diophantine Number Theory

作者：Jan-Hendrik Evertse 出版社：Cambridge Univ Pr 出版日：2016/10/01 裝訂：精裝

Discriminant equations are an important class of Diophantine equations with close ties to algebraic number theory, Diophantine approximation and Diophantine geometry. This book is the first comprehensive account of discriminant equations and their applications. It brings together many aspects, including effective results over number fields, effective results over finitely generated domains, estimates on the number of solutions, applications to algebraic integers of given discriminant, power integral bases, canonical number systems, root separation of polynomials and reduction of hyperelliptic curves. The authors' previous title, Unit Equations in Diophantine Number Theory, laid the groundwork by presenting important results that are used as tools in the present book. This material is briefly summarized in the introductory chapters along with the necessary basic algebra and algebraic number theory, making the book accessible to experts and young researchers alike.

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7.

Factorization Algebras in Quantum Field Theory

作者：Kevin Costello 出版社：Cambridge Univ Pr 出版日：2016/12/31 裝訂：精裝

Factorization algebras are local-to-global objects that play a role in classical and quantum field theory which is similar to the role of sheaves in geometry: they conveniently organize complicated information. Their local structure encompasses examples like associative and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In this first volume, the authors develop the theory of factorization algebras in depth, but with a focus upon examples exhibiting their use in field theory, such as the recovery of a vertex algebra from a chiral conformal field theory and a quantum group from Abelian Chern-Simons theory. Expositions of the relevant background in homological algebra, sheaves and functional analysis are also included, thus making this book ideal for researchers and graduates working at the interface between mathematics and physics.

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8.

Symplectic Topology and Floer Homology

作者：Yong-Geun Oh 出版社：Cambridge Univ Pr 出版日：2015/08/31 裝訂：精裝

Published in two volumes, this is the first book to provide a thorough and systematic explanation of symplectic topology, and the analytical details and techniques used in applying the machinery arising from Floer theory as a whole. Volume 1 covers the basic materials of Hamiltonian dynamics and symplectic geometry and the analytic foundations of Gromov's pseudoholomorphic curve theory. One novel aspect of this treatment is the uniform treatment of both closed and open cases and a complete proof of the boundary regularity theorem of weak solutions of pseudo-holomorphic curves with totally real boundary conditions. Volume 2 provides a comprehensive introduction to both Hamiltonian Floer theory and Lagrangian Floer theory. Symplectic Topology and Floer Homology is a comprehensive resource suitable for experts and newcomers alike.

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9.

Symplectic Topology and Floer Homology

作者：Yong-Geun Oh 出版社：Cambridge Univ Pr 出版日：2015/09/15 裝訂：精裝

Published in two volumes, this is the first book to provide a thorough and systematic explanation of symplectic topology, and the analytical details and techniques used in applying the machinery arising from Floer theory as a whole. Volume 2 provides a comprehensive introduction to both Hamiltonian Floer theory and Lagrangian Floer theory, including many examples of their applications to various problems in symplectic topology. The first volume covered the basic materials of Hamiltonian dynamics and symplectic geometry and the analytic foundations of Gromov's pseudoholomorphic curve theory. Symplectic Topology and Floer Homology is a comprehensive resource suitable for experts and newcomers alike.

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10.

Symplectic Topology and Floer Homology

作者：Yong-Geun Oh 出版社：Cambridge Univ Pr 出版日：2015/08/31 裝訂：精裝

Published in two volumes, this is the first book to provide a thorough and systematic explanation of symplectic topology, and the analytical details and techniques used in applying the machinery arising from Floer theory as a whole. Volume 1 covers the basic materials of Hamiltonian dynamics and symplectic geometry and the analytic foundations of Gromov's pseudo-holomorphic curve theory. One novel aspect of this treatment is the uniform treatment of both closed and open cases and a complete proof of the boundary regularity theorem of weak solutions of pseudo-holomorphic curves with totally real boundary conditions. Volume 2 provides a comprehensive introduction to both Hamiltonian Floer theory and Lagrangian Floer theory, including many examples of their applications to various problems in symplectic topology. Symplectic Topology and Floer Homology is a comprehensive resource suitable for experts and newcomers alike.

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11.

The Theory of H(b) Spaces

作者：Emmanuel Fricain 出版社：Cambridge Univ Pr 出版日：2014/07/01 裝訂：精裝

An H(b) space is defined as a collection of analytic functions which are in the image of an operator. The theory of H(b) spaces bridges two classical subjects: complex analysis and operator theory, which makes it both appealing and demanding. The first volume of this comprehensive treatment is devoted to the preliminary subjects required to understand the foundation of H(b) spaces, such as Hardy spaces, Fourier analysis, integral representation theorems, Carleson measures, Toeplitz and Hankel operators, various types of shift operators, and Clark measures. The second volume focuses on the central theory. Both books are accessible to graduate students as well as researchers: each volume contains numerous exercises and hints, and figures are included throughout to illustrate the theory. Together, these two volumes provide everything the reader needs to understand and appreciate this beautiful branch of mathematics.

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12.

Sobolev Spaces on Metric Measure Spaces ― An Approach Based on Upper Gradients

作者：Juha Heinonen 出版社：Cambridge Univ Pr 出版日：2015/03/31 裝訂：精裝

Analysis on metric spaces emerged in the 1990s as an independent research field providing a unified treatment of first-order analysis in diverse and potentially nonsmooth settings. Based on the fundamental concept of upper gradient, the notion of a Sobolev function was formulated in the setting of metric measure spaces supporting a Poincaré inequality. This coherent treatment from first principles is an ideal introduction to the subject for graduate students and a useful reference for experts. It presents the foundations of the theory of such first-order Sobolev spaces, then explores geometric implications of the critical Poincaré inequality, and indicates numerous examples of spaces satisfying this axiom. A distinguishing feature of the book is its focus on vector-valued Sobolev spaces. The final chapters include proofs of several landmark theorems, including Cheeger's stability theorem for Poincaré inequalities under Gromov–Hausdorff convergence, and the Keith–Zhong self-improvement

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13.

Pseudo-reductive Groups

作者：Brian Conrad 出版社：Cambridge Univ Pr 出版日：2015/04/30 裝訂：精裝

Pseudo-reductive groups arise naturally in the study of general smooth linear algebraic groups over non-perfect fields and have many important applications. This monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. In this second edition there is new material on relative root systems and Tits systems for general smooth affine groups, including the extension to quasi-reductive groups of famous simplicity results of Tits in the semisimple case. Chapter 9 has been completely rewritten to describe and classify pseudo-split absolutely pseudo-simple groups with a non-reduced root system over arbitrary fields of characteristic 2 via the useful new notion of 'minimal type' for pseudo-reductive groups. Researchers and graduate students working in related areas, such as algebraic geometry, algebraic group theory, or number theory will value this book, as it develops tools likely to be used in tackling other

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14.

Monopoles and Three-Manifolds

作者：Peter Kronheimer 出版社：Cambridge Univ Pr 出版日：2010/11/25 裝訂：平裝

Originating with Andreas Floer in the 1980s, Floer homology has proved to be an effective tool in tackling many important problems in three- and four-dimensional geometry and topology. This 2007 book provides a comprehensive treatment of Floer homology, based on the Seiberg–Witten monopole equations. After first providing an overview of the results, the authors develop the analytic properties of the Seiberg–Witten equations, assuming only a basic grounding in differential geometry and analysis. The Floer groups of a general three-manifold are then defined and their properties studied in detail. Two final chapters are devoted to the calculation of Floer groups and to applications of the theory in topology. Suitable for beginning graduate students and researchers, this book provides a full discussion of a central part of the study of the topology of manifolds.

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15.

Hilbert's Tenth Problem：Diophantine Classes and Extensions to Global Fields

作者：Alexandra Shlapentokh 出版社：Cambridge Univ Pr 出版日：2006/11/09 裝訂：精裝

In the late sixties Matiyasevich, building on the work of Davis, Putnam and Robinson, showed that there was no algorithm to determine whether a polynomial equation in several variables and with integer coefficients has integer solutions. Hilbert gave finding such an algorithm as problem number ten on a list he presented at an international congress of mathematicians in 1900. Thus the problem, which has become known as Hilbert's Tenth Problem, was shown to be unsolvable. This book presents an account of results extending Hilbert's Tenth Problem to integrally closed subrings of global fields including, in the function field case, the fields themselves. While written from the point of view of Algebraic Number Theory, the book includes chapters on Mazur's conjectures on topology of rational points and Poonen's elliptic curve method for constructing a Diophatine model of rational integers over a 'very large' subring of the field of rational numbers.

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16.

Free Ideal Rings and Localization in General Rings

作者：P. M. Cohn 出版社：Cambridge Univ Pr 出版日：2006/06/08 裝訂：精裝

Proving that a polynomial ring in one variable over a field is a principal ideal domain can be done by means of the Euclidean algorithm, but this does not extend to more variables. However, if the variables are not allowed to commute, giving a free associative algebra, then there is a generalization, the weak algorithm, which can be used to prove that all one-sided ideals are free. This book presents the theory of free ideal rings (firs) in detail. Particular emphasis is placed on rings with a weak algorithm, exemplified by free associative algebras. There is also a full account of localization which is treated for general rings but the features arising in firs are given special attention. Each section has a number of exercises, including some open problems, and each chapter ends in a historical note.

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17.

Theory of Finite Simple Groups

作者：Gerhard O. Michler 出版社：Cambridge University Press 出版日：2006/09/21 裝訂：平裝

This book provides the first representation theoretic and algorithmic approach to the theory of abstract finite simple groups. Concrete applications are demonstrated in the construction of the simple

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18.

Harmonic Measure

作者：John B. Garnett 出版社：Cambridge Univ Pr 出版日：2005/06/09 裝訂：精裝

During the last two decades several remarkable new results were discovered about harmonic measure in the complex plane. This book provides a careful survey of these results and an introduction to the branch of analysis which contains them. Many of these results, due to Bishop, Carleson, Jones, Makarov, Wolff and others, appear here in paperback for the first time. The book is accessible to students who have completed standard graduate courses in real and complex analysis. The first four chapters provide the needed background material on univalent functions, potential theory, and extremal length, and each chapter has many exercises to further inform and teach the readers.

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19.

Non-Hausdorff Topology and Domain Theory ─ Selected Topics in Point-Set Topology

作者：Jean Goubault-Larrecq 出版社：Cambridge Univ Pr 出版日：2013/05/31 裝訂：精裝

This unique book on modern topology looks well beyond traditional treatises and explores spaces that may, but need not, be Hausdorff. This is essential for domain theory, the cornerstone of semantics of computer languages, where the Scott topology is almost never Hausdorff. For the first time in a single volume, this book covers basic material on metric and topological spaces, advanced material on complete partial orders, Stone duality, stable compactness, quasi-metric spaces and much more. An early chapter on metric spaces serves as an invitation to the topic (continuity, limits, compactness, completeness) and forms a complete introductory course by itself. Graduate students and researchers alike will enjoy exploring this treasure trove of results. Full proofs are given, as well as motivating ideas, clear explanations, illuminating examples, application exercises and some more challenging problems for more advanced readers.

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20.

Differential Geometry of Singular Spaces and Reduction of Symmetry

作者：J. Śniatycki 出版社：Cambridge Univ Pr 出版日：2013/07/31 裝訂：精裝

In this book the author illustrates the power of the theory of subcartesian differential spaces for investigating spaces with singularities. Part I gives a detailed and comprehensive presentation of the theory of differential spaces, including integration of distributions on subcartesian spaces and the structure of stratified spaces. Part II presents an effective approach to the reduction of symmetries. Concrete applications covered in the text include reduction of symmetries of Hamiltonian systems, non-holonomically constrained systems, Dirac structures, and the commutation of quantization with reduction for a proper action of the symmetry group. With each application the author provides an introduction to the field in which relevant problems occur. This book will appeal to researchers and graduate students in mathematics and engineering.

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K-stability of Fano Varieties

Abstract Chiral Polytopes

Homotopy Theory of Higher Categories

Entropy in Dynamical Systems

Factorization Algebras in Quantum Field Theory

Discriminant Equations in Diophantine Number Theory

Factorization Algebras in Quantum Field Theory

Symplectic Topology and Floer Homology

Symplectic Topology and Floer Homology

Symplectic Topology and Floer Homology

The Theory of H(b) Spaces

Sobolev Spaces on Metric Measure Spaces ― An Approach Based on Upper Gradients

Pseudo-reductive Groups

Monopoles and Three-Manifolds

Hilbert's Tenth Problem：Diophantine Classes and Extensions to Global Fields

Free Ideal Rings and Localization in General Rings

Theory of Finite Simple Groups

Harmonic Measure

Non-Hausdorff Topology and Domain Theory ─ Selected Topics in Point-Set Topology

Differential Geometry of Singular Spaces and Reduction of Symmetry