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34925 results in Mathematics (general)

Page 1 of 1747

Differential Topology
  • Gereon Quick
  • Coming soon
  • Expected online publication date:
    September 2026
    Print publication:
    30 September 2026
  • Differential topology uncovers the hidden structure of smooth spaces –the foundation of modern geometry and topology. This book offers a clear, rigorous introduction to the subject, blending theory with concrete examples and applications. Beginning with the basics of manifolds and smooth maps, it develops essential tools and concepts such as tangent spaces, transversality, cobordism, and tubular neighbourhoods, before progressing to powerful invariants like the Brouwer degree, intersection numbers, and the Hopf invariant. Along the way, readers encounter landmark results including Whitney's embedding theorem, Brouwer's fixed point theorem, the Pontryagin construction, Hopf's degree theorem, and the Poincaré–Hopf index theorem. Each chapter combines intuitive explanations with precise and detailed proofs, supported by exercises and detailed solutions that deepen understanding. Ideal for advanced undergraduates, graduate students, and researchers, this text provides a gateway to one of mathematics' most elegant and influential fields – where analysis, geometry, and topology meet.

Periodic Elliptic Partial Differential Operators
  • The Main Structures
  • Volume 1
  • Peter Kuchment
  • Coming soon
  • Expected online publication date:
    September 2026
    Print publication:
    30 September 2026
  • The study of periodic partial differential equations has experienced significant growth in recent decades, driven by emerging applications in fields such as photonic crystals, metamaterials, fluid dynamics, carbon nanostructures, and topological insulators. This book provides a uniquely comprehensive overview for mathematicians, physicists, and material scientists engaged in the analysis and construction of periodic media. It describes all the mathematical objects, tools, problems, and techniques involved. Topics covered are central for areas such as spectral theory of PDEs, homogenization, condensed matter physics and optics. Although it is not a textbook, some basic proofs, background material, and references to an extensive bibliography providing pointers to the wider literature are included to allow graduate students to access the content.

Spectra of Signed Graphs
  • Zoran Stanić
  • Coming soon
  • Expected online publication date:
    August 2026
    Print publication:
    31 August 2026
  • This monograph extends the classical spectral theory of ordinary graphs to the broader framework of signed graphs. It integrates foundational results with recent advances, explores applications, and clarifies connections with related mathematical structures while indicating promising directions for future research. The exposition remains rigorous throughout, presenting core concepts, major developments, and emerging ideas in a coherent and accessible manner. Complementing the theoretical material, the monograph includes illustrative examples and problem sections to support understanding and encourage continued study. This monograph will serve as a reference for mathematicians working in the spectral theory of signed graphs as well as a tutorial for graduate students entering the subject area and computer scientists, chemists, physicists, biologists, electrical engineers and others whose work involves graph-based modelling.

Birational Geometry and Manin's Conjecture
  • Sho Tanimoto
  • Coming soon
  • Expected online publication date:
    July 2026
    Print publication:
    31 July 2026
  • This book provides the first comprehensive study of the geometric aspects of Manin's conjecture. It equips the reader with a working knowledge of higher dimensional algebraic geometry, including the minimal model program and its applications to arithmetic and Diophantine geometry. The text also develops the foundations of the moduli theory of rational curves on Fano varieties and explores its role in the geometric formulation of Manin's conjecture, supported by worked examples. The book is suitable for graduates and researchers in arithmetic geometry seeking a modern introduction to birational geometry and the moduli theory of rational curves. It will also interest experts in higher‑dimensional algebraic geometry who wish to understand recent applications of these techniques to arithmetic geometry.

Dilation and Model Theory for Pairs of Commuting Contraction Operators
  • Joseph A. Ball, Haripada Sau
  • Coming soon
  • Expected online publication date:
    July 2026
    Print publication:
    31 July 2026
  • Exactly a decade after the publication of the Sz.-Nagy Dilation Theorem, Tsuyoshi Andô proved that, just like for a single contractive operator, every commuting pair of Hilbert-space contractions can be lifted to a commuting isometric pair. Although the inspiration for Andô's proof comes from the elegant construction of Schäffer for the single-variable case, his proof did not shed much light on the explicit nature of the dilation operators and the dilation space as did the original Schäffer and Douglas constructions for a single contraction. Consequently, there has been little follow-up in the direction of a more systematic extension of the Sz.-Nagy–Foias dilation and model theory to the bi-variate setting. Sixty years since the appearance of Andô's first step comes this thorough systematic treatment of a dilation and model theory for pairs of commuting contractions.

Equivariant Principal ∞-Bundles
  • Hisham Sati, Urs Schreiber
  • Coming soon
  • Expected online publication date:
    July 2026
    Print publication:
    30 June 2026
  • Principal bundles and their associated fiber bundles famously play a foundational role in both algebraic and differential topology, as well as in fundamental and solid-state physics. More recently, their equivariant and higher homotopy enhancements (gerbes) have been crucial in generalized cohomology theory and for the physics of extended solitons and topological phases. This text is the first to offer a unified perspective of, and introduction to, these topics, providing an insight into material previously scattered across the literature. After a self-contained account of the classical theory of equivariant principal bundles in modern topological groupoid language, the book develops, on the novel backdrop of cohesive higher topos theory, a powerful theory of equivariant principal higher bundles. It establishes new methods like the 'smooth Oka principle' and 'twisted Elmendorf theorem' to elegantly prove classification results and clarify the relation to proper equivariant generalized cohomology theories.

A Primer, and Beyond, on Composition Operators on the Unit Disk
  • Pascal Lefèvre, Hervé Queffélec
  • Coming soon
  • Expected online publication date:
    June 2026
    Print publication:
    30 June 2026
  • This is a contemporary treatment of composition operators on Banach spaces of analytic functions in one complex variable. It provides a step-by-step introduction, starting with a review (including full proofs) of the key tools needed, and building the theory with a focus on Hardy and Bergman spaces. Several proofs of operator boundedness (Littlewood's principle) are given, and the authors discuss approaches to compactness issues and essential norm estimates (Shapiro's theorem) using different tools such as Carleson measures and Nevanlinna counting functions. Membership of composition operators in various ideal classes (Schatten classes for instance) and their singular numbers are studied. This framework is extended to Hardy-Orlicz and Bergman-Orlicz spaces and finally, weighted Hardy spaces are introduced, with a full characterization of those weights for which all composition operators are bounded. This will be a valuable resource for researchers and graduate students working in functional analysis, operator theory, or complex analysis.

Surveys in Combinatorics 2026
  • Edited by Andrei Gagarin, Roger Behrend, Matthew Lettington, Iskander Aliev
  • Coming soon
  • Expected online publication date:
    June 2026
    Print publication:
    30 June 2026
  • This volume contains eight survey articles by the invited speakers of the 31st British Combinatorial Conference, held at Cardiff University in July 2026. Each article provides an overview of recent developments in a current hot research topic in combinatorics. Topics covered include random planar graphs, temporal graphs, domino tilings, extremal poset theory, asymptotic enumeration, graph homomorphisms, combinatorial rigidity theory, logic and model theory, matroids, and graph bootstrap percolation. The authors are among the world's foremost researchers on their respective topics, but their surveys are accessible to nonspecialist readers: they are written clearly, with little prior knowledge assumed, and with pointers to the wider literature. Taken together, these surveys give a snapshot of the research frontier in contemporary combinatorics, helping researchers and graduate students in mathematics and theoretical computer science to keep abreast of the latest developments in the field.

Ramification Groups of Local Fields
  • with Geometric Applications
  • Takeshi Saito
  • Coming soon
  • Expected online publication date:
    June 2026
    Print publication:
    31 May 2026
  • Ramification groups of local fields are essential tools for studying boundary behaviour in geometric objects and the degeneration of Galois representations. This book presents a comprehensive development of the recently established theory of upper ramification groups of local fields with imperfect residue fields, starting from the foundations. It also revisits classical theory, including the Hasse–Arf theorem, and offers an optimal generalisation via log monogenic extensions. The conductor of Galois representations, defined through ramification groups, has numerous geometric applications, notably the celebrated Grothendieck–Ogg–Shafarevich formula. A new proof of the Deligne–Kato formula is also provided; this result plays a pivotal role in the theory of characteristic cycles. With a foundational understanding of commutative rings and Galois theory, graduate students and researchers will be well-equipped to engage with this rich area of arithmetic geometry.

The Shrikhande Graph
  • A Window on Discrete Mathematics
  • Peter J. Cameron, Aparna Lakshmanan S., Ambat Vijayakumar
  • Coming soon
  • Expected online publication date:
    May 2026
    Print publication:
    31 May 2026
  • The Shrikhande graph, discovered by Indian Mathematician Sharadchandra Shankar Shrikhande in 1959, exhibits several unusual properties and occupies a pivotal position within discrete mathematics. Offering a unique introduction to graph theory and discrete mathematics, this book uses the example of the Shrikhande graph as a window through which these topics can be explored. Providing historical background, including the Euler conjecture and its demise, the authors explore key concepts including: Cayley graphs; topological graph theory; spectral theory; Latin squares; root systems. A novel and valuable resource for graduate students and researchers interested in graph theory, its history, and applications, this book offers a comprehensive exploration of the Shrikhande graph and its significance.
Computability and Computational Explanation

Computability and Computational Explanation
  • André Curtis-Trudel
  • Coming soon
  • Expected online publication date:
    May 2026
    Print publication:
    31 May 2026
  • This Element is an introduction to classical computability theory and scientific efforts to use computability-theoretic notions to explain empirical phenomena. It is written for advanced undergraduates and graduate students in philosophy, assuming no prior exposure to computability theory. Its goals are threefold: (1) to introduce some important theoretical tools and results from classical computability theory; (2) to survey some of the ways these have been used to support explanatory projects in computer and cognitive science; and (3) to outline a few of the more prominent philosophical debates surrounding these projects.

Celestial Mechanics
  • Classical and Modern Methods
  • Antonio Giorgilli, Ugo Locatelli, Marco Sansottera
  • Coming soon
  • Expected online publication date:
    May 2026
    Print publication:
    31 May 2026
  • Starting from ancient astronomy, this text follows the development of celestial mechanics culminating in applications of the most recent results concerning stability of planetary orbits: Kolmogorov's and Nekhoroshev's theorems. Key topics covered include: a historical introduction from ancient astronomy to Kepler and Newton; Lagrange's perturbation theory; the problem of three bodies, with a discussion of Levi-Civita regularization and of Sundman's theorem; methods of algebraic calculation of perturbation series, including a discussion of non-convergence due to the accumulation of small divisors; and a complete application of Kolmogorov's and Nekhoroshev's theorems. Written in an accessible, self-contained way with few prerequisites, this book can serve as an introductory text for senior undergraduate and graduate students, and for young researchers. Its approach allows students to learn about perturbation methods leading to advanced results.

The Geometry of Jet Bundles
  • 2nd edition
  • D. J. Saunders
  • Coming soon
  • Expected online publication date:
    May 2026
    Print publication:
    31 May 2026
  • Now in its second edition, this book provides a detailed introduction to the theory of jet bundles. It is written for mathematicians and physicists who wish to study differential equations, particularly those associated with the calculus of variations, in a modern geometric way. A knowledge of differential geometry is assumed, although introductory chapters include the necessary background of fibred manifolds, and on vector and affine bundles. The book explores how first-order jets may be considered as the natural generalisation of vector fields for studying variational problems in field theory, and so many of the constructions are introduced in the context of first- or second-order jets, before being described in their full generality. It features a proof of the local exactness of the variational bicomplex. This edition includes new chapters on velocity bundles and bundles of contact elements, together with updated material on the calculus of variations.

Multifunctorial Equivariant Algebraic K-Theory
  • Donald Yau
  • Coming soon
  • Expected online publication date:
    May 2026
    Print publication:
    31 May 2026

Locally Flat Embeddings of 3-Manifolds in S4
  • Jonathan Hillman
  • Coming soon
  • Expected online publication date:
    April 2026
    Print publication:
    31 May 2026
  • The study of smooth embeddings of 3-manifolds in 4-space has been hampered by difficulties with the simplest case, that of homology spheres. This book presents some advantages of working with locally flat embeddings. The first two chapters outline the tools used and give general results on embeddings of 3-manifolds in S4. The next two chapters consider which Seifert manifolds may embed, with criteria in terms of Seifert data. After summarizing results on those Seifert manifolds that embed smoothly, the following chapters determine which 3-manifolds with virtually solvable fundamental groups embed. The final three chapters study the complementary regions. When these have 'good' fundamental groups, topological surgery may be used to find homeomorphisms. Figures throughout help illustrate links representing embeddings and open questions are further discussed in the appendices, making this a valuable resource for graduate students and research workers in geometric topology.

Spectra of Discrete Structures
  • Jürgen Jost, Raffaella Mulas, Dong Zhang
  • Coming soon
  • Expected online publication date:
    April 2026
    Print publication:
    30 April 2026
  • Addressing the active and challenging field of spectral theory, this book develops the general theory of spectra of discrete structures, on graphs, simplicial complexes, and hypergraphs. In fact, hypergraphs have long been neglected in mathematical research, but because of the discovery of Laplace operators that can probe their structure, and their manifold applications from chemical reaction networks to social interactions, they have now become one of the most active areas of interdisciplinary research. The authors' analysis of spectra of discrete structures embeds intuitive and easily visualized examples, which are often quite subtle, within a general mathematical framework. They highlight novel research on Cheeger-type inequalities that connect spectral estimates with the geometry, more precisely the cohesion, of the underlying structure. Establishing mathematical foundations and demonstrating applications, this book will be of interest to graduate students and researchers in mathematics working on the spectral theory of operators on discrete structures.

Extremal Graph and Hypergraph Theory
  • With Ramsey Theory
  • Dhruv Mubayi, Jacques A. Verstraete
  • Coming soon
  • Expected online publication date:
    April 2026
    Print publication:
    30 April 2026
  • Providing a cohesive reference for advanced undergraduates, graduate students and even experienced researchers, this text contains both introductory and advanced material in extremal graph theory, hypergraph theory and Ramsey theory. Along the way, the book includes many modern proof techniques in the field such as the probabilistic method and algebraic methods. Several recent breakthroughs are presented with complete proofs, for example, recent results on the sunflower problem, and off-diagonal and geometric Ramsey theory. It is perhaps unique in containing material on both hypergraph regularity and containers. Featuring an extensive list of exercises, the text is suitable as a teaching text for a variety of courses in extremal combinatorics. Each of the two parts can form the basis of separate courses, and the majority of sections are designed to match the length of a single lecture.

Multiplicative Number Theory II
  • Primes and Sieves
  • Hugh L. Montgomery, Robert C. Vaughan
  • Coming soon
  • Expected online publication date:
    April 2026
    Print publication:
    09 April 2026
  • This long-anticipated work shares the aims of its celebrated companion: namely, to provide an introduction for students and a reference for researchers to the techniques, results, and terminology of multiplicative number theory. This volume builds on the earlier one (which served as an introduction to basic, classical results) and focuses on sieve methods. This area has witnessed a number of major advances in recent years, e.g. gaps between primes, large values of Dirichlet polynomials and zero density estimates, all of which feature here. Despite the fact that the book can serve as an entry to contemporary mathematics, it remains largely self-contained, with appendices containing background or material more advanced than undergraduate mathematics. Again, exercises, of which there is a profusion, illustrate the theory or indicate ways in which it can be developed. Each chapter ends with a thorough set of references, which will be essential for all analytic number theorists.

Sets and Transfinite Algebra
  • Thomas Müller
  • Coming soon
  • Expected online publication date:
    April 2026
    Print publication:
    09 April 2026
  • This two-part book offers a rigorous yet accessible exploration of set theory and transfinite algebra, with a particular emphasis on the axiom of choice and its applications. Part I presents an informal axiomatic introduction to the foundations of set theory, including a detailed treatment of the axiom of choice and its equivalents, suitable for advanced undergraduates. Part II, aimed at graduate students and professional mathematicians, treats selected topics in transfinite algebra where the axiom of choice, in one form or another, is useful or even indispensable. The text features self-contained chapters for flexible use, and includes material rarely found in the literature, such as Tarski's work on complete lattices, Hamel's solution to Cauchy's functional equation, and Artin's resolution of Hilbert's 17th problem. Over 140 exercises, with full solutions provided in the Appendix, support active engagement and deeper understanding, making this a valuable resource for both independent study and course preparation.

Topics in Number Theory
  • Jorge Morales
  • Coming soon
  • Expected online publication date:
    March 2026
    Print publication:
    09 April 2026
  • Spanning elementary, algebraic, and analytic approaches, this book provides an introductory overview of essential themes in number theory. Designed for mathematics students, it progresses from undergraduate-accessible material requiring only basic abstract algebra to graduate-level topics demanding familiarity with algebra and complex analysis. The first part covers classical themes: congruences, quadratic reciprocity, partitions, cryptographic applications, and continued fractions with connections to quadratic Diophantine equations. The second part introduces key algebraic tools, including Noetherian and Dedekind rings, then develops the finiteness of class groups in number fields and the analytic class number formula. It also examines quadratic fields and binary quadratic forms, presenting reduction theory for both definite and indefinite cases. The final section focuses on analytic methods: L-series, primes in arithmetic progressions, and the Riemann zeta function. It addresses the Prime Number Theorem and explicit formulas of von Mangoldt and Riemann, equipping students with foundational knowledge across number theory's major branches.

Page 1 of 1747