Series: Cambridge Tracts in Mathematics
Published: July 2026
Format: Hardback
ISBN: 9781009611633
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.
Develops the geometric aspects of Manin's conjecture
Introduces applications of higher-dimensional algebraic geometry to arithmetic geometry
Serves as a practical learning resource for arithmetic geometers interested in a modern theory of birational geometry
Preface
Acknowledgements
1. Introduction
2. Height functions
3. Quick introduction to higher-dimensional algebraic geometry
4. Manin's conjecture
5. Proofs of main results
6. Further examples
7. Moduli of rational curves
8. Examples of geometric Manin's conjecture II
References
Index.
Published: July 2026
Format: Hardback
ISBN: 9781009382526
Mathematicians, physicists, engineers, and data scientists will welcome this comprehensive, practical guide to computing spectral properties of operators in infinite-dimensional settings with rigorous guarantees. It explains why standard discretisation can fail and shows how to overcome these pitfalls. It develops resolvent-based algorithms with provable convergence and certified error bounds, organised by a precise computability classification that clarifies what is achievable, what is impossible, and what extra information makes problems tractable. Topics include spectra and pseudospectra, spectral measures and functional calculus, spectral types, fractal and Cantor-type spectra, essential versus discrete spectra and multiplicities, spectral radii, abscissas and gaps, nonlinear operator pencils, and verified computation. A distinctive feature is the integration of modern applications, including a fully rigorous treatment of data-driven Koopman spectral analysis. Hundreds of worked examples, exercises with solutions, notes, and usable code make the book both a reference and a practical toolkit for researchers and students.
Explores certified, implementable algorithms for infinite-dimensional spectral properties
Provides a unified 'foundations > algorithms > limits' framework (SCI), with a complete map of what is possible and impossible
State-of-the-art scope, including the first fully rigorous treatment of modern data-driven spectral methods
Features a huge range of worked examples and applications across disciplines, with usable code accompanying all examples
Preface
Notation
Example classifications for spectral sets
1. Spectral problems in infinite dimensions
2. The solvability complexity index: a toolkit for classifying problems
3. Computing spectra with error control
4. Spectral measures of self-adjoint operators
5. Spectral measures of unitary operators
6. Spectral types of self-adjoint and unitary operators
7. Quantifying the size of spectra
8. Essential spectra
9. Spectral radii, abscissas, and gaps
10. Nonlinear spectral problems
11. Data-driven Koopman spectral problems for nonlinear dynamical systems
A. Some brief preliminaries
B. A bluffer's guide to the SCI hierarchy
Bibliography
Index.
*
Series: London Mathematical Society Lecture Note Series
Published: August 2026
Format: Paperback
ISBN: 9781009853347
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.
Explores, elaborates, and synthesizes the most significant results in the spectral theory of signed graphs
Introduces the theory step-by-step with accessible explanations and illustrative examples
Highlights generalizations and applications across mathematical and non-mathematical
disciplines
Preface
1. Introduction
2. Eigenvalues
3. Strong regularity
4. Star complements
5. Signed line graphs
6. Signed graphs with a small number of eigenvalues
7. Integrality and cospectrality
8. Polynomial reconstruction
9. Related structures
10. Generalizations
References
Index.
Series: Cambridge Studies in Advanced Mathematics
Published: September 2026
Format: Hardback
ISBN: 9781009282420
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.
A unique and valuable resource for mathematicians, physicists, and material scientists, describing the main objects, problems, tools, and techniques arising in the area
Describes the challenges and approaches arising in a variety of theoretical and applied problems coming from various areas including spectral theory of PDEs, homogenization, condensed matter physics and optics
Surveys the classical one-dimension case first and provides many references to the relevant literature
Preface
Introduction
Tentative contents of the planned sequel
1. Periodic ordinary differential operators
2. Multidimensional periodicity: lattices, fundamental domains, Fourier series
3. Floquet transform and direct integral decomposition
4. Dispersion relations, Bloch, Fermi and Floquet varieties
5. Spectral structure of periodic elliptic operators
6. Localized perturbations of periodic operators
7. Wannier functions
8. Operators on Abelian coverings of compact manifolds
Appendix A. Some information from complex analysis
Appendix B. Some information from functional analysis and operator theory
Appendix C. Operator-functions
Appendix D. Banach (locally trivial) vector bundles
Appendix E. The Landis conjecture
Appendix F. Proofs of some technical statements
References
Index.
Copyright 2026
Hardback
ISBN 9781041117520
246 Pages 87 Color Illustrations
Theory, experiments, computation, and data are considered as the four pillars of science and engineering. Experimental Design for Data Science and Engineering describes efficient statistical methods for making the experiments cheaper and computations faster for extracting valuable information from data and help identify discrepancies in the theory. The book also includes recent advances in experimental designs for dealing with large amounts of observational data.
Traditionally the design and analysis of physical and computer experiments are treated differently, but this book attempts to create a unified framework using Gaussian process models. Although optimal designs are formulated using Gaussian process models, the focus is on obtaining practical experimental designs that are robust to model assumptions. A wide variety of topics are covered in the book -- from designs for interpolating or integrating simple functions to designs that are useful for optimizing and calibrating complex computer models. It draws techniques that are spread across the fields of statistics, applied mathematics, operations research, uncertainty quantification, and information theory, and build experimental design as a fundamental data analytic tool for engineering and scientific discoveries.
Designs for both computer and physical experiments are discussed in a unified framework.
Integrates several concepts from numerical analysis, Monte Carlo methods, sensitivity analysis, optimization, and machine learning with experimental design techniques in statistics.
Methods are explained using many real experiments from physical sciences and engineering.
Experimental design techniques for analysis and compression of big data are discussed.
All the numerical illustrations in the book are reproducible using R and Python codes provided in the author’s GitHub site.
Preface
Section I: Introduction
Chapter 1: Experiments
1.1 Overview
1.2 Applications
1.3 Role of Uncertainty
1.4 Outline of the Book
Chapter 2: Modeling Techniques
2.1 Interpolation
2.2 Regression
Section II: Computer Experiments
Chapter 3: Model-based Designs
3.1 Prediction-based Designs
3.2 Maximum Entropy Designs
Chapter 4: Space-Filling Designs
4.1 Clustering-based designs
4.2 Minimax Designs
4.3 Maximin Designs
4.4 Latin Hypercube Designs
4.5 MaxPro Designs
4.6 Minimum Energy Designs
Chapter 5: Representative Points
5.1 Uniform Design
5.2 Non-uniform Distributions
Chapter 6: Screening Designs
6.1 Sensitivity Analysis
6.2 Morris Screening Design
6.3 MOFAT designs
Chapter 7: Sequential Designs
7.1 Emulation
7.2 Optimization
7.3 Inverse Designs
Section III: Physical Experiments
Chapter 8: Fractional Factorial Designs
8.1 Two-level Designs
8.2 Bayesian-inspired Designs
8.3 Designs with More than Two Levels
8.4 Mixture Designs
Chapter 9: Model Calibration
9.1 Nonlinear Optimal Designs
9.2 Robust Designs
Section IV: Data Science
Chapter 10: Data Subsampling
10.1 Support Points-based Subsampling
10.2 Data Splitting
10.3 Data Twinning
10.4 Supervised Compression
Chapter 11: Data Analysis
11.1 Factor Selection and Ranking
11.2 Twin-Gaussian Process
Bibliography
Index
*
Copyright 2026
Hardback
ISBN 9781041216834
218 Pages 1 Color & 99 B/W Illustrations
April 16, 2026 by Chapman & Hall
This book is an ambitious but optimistic treatment of the subject of topology. Not only does Elements of Topology: Theory and Practice, Second Edition treat the standard basic material on point-set topology, but it also gives an introduction to algebraic topology, a treatment of manifolds, a discussion of function spaces, and some ideas of knot theory. Even the exciting new topic of the Jones polynomial is covered. After discussing the key ideas of topology, the author examines the more advanced topics of algebraic topology and manifold theory.
Topic coverage has been reduced in this second edition, and exercise sets have been added at the end of each section. The book as a whole—and the first two chapters in particular— offer many examples. Solutions to selected exercises are included at the end.
Today’s students need a text that speaks to them in their own language, and at a pace with which they are comfortable. That is the goal of this edition. Taking a fresh and accessible approach to a venerable subject, this text provides excellent representations of topological ideas. It forms the foundation for further mathematical study in real analysis, abstract algebra, and beyond.
1. Fundamentals
1.1 What Is Topology?
1.2 First Definitions
1.3 Mappings
1.4 The Separation Axioms
1.5 Compactness
1.6 Homeomorphisms
1.7 Connectedness
1.8 Path-Connectedness
1.9 Continua
1.10 Totally Disconnected Spaces
1.11 The Cantor Set
1.12 Metric Spaces
1.13 Metrizability
1.14 Baire’s Theorem
1.15 Lebesgue’s Lemma and Lebesgue Numbers
2. Advanced Properties
2.1 Basis and Sub-Basis
2.2 Product Spaces
2.3 Relative Topology
2.4 First Countable and Second Countable
2.5 Compactifications
2.6 Quotient Topologies
2.7 Uniformities
2.8 Proper Mappings
2.9 Paracompactness
3. Basic Algebraic Topology
3.1 Homotopy Theory
3.2 Homology Theory
3.3 Covering Spaces
3.4 The Concept of Index
4. Manifold Theory
4.1 Basic Concepts
4.2 The Definition
5. Function Spaces
5.1 Preliminary Ideas
5.2 The Topology of Pointwise Convergence
5.3 The Compact-Open Topology
5.4 Uniform Convergence
5.5 Equicontinuity and the Ascoli-Arzela Theorem
5.6 The Weierstrass Approximation Theorem
6. Knot Theory
6.1 What Is a Knot?
6.2 The Alexander Polynomial
6.3 The Jones Polynomial
Solutions of Selected Exercises
This volume contains articles from the lectures of the 29th Gökova Geometry-Topology Conference, held on the Gökova Bay from May 27 to May 31, 2024. It contains three inspiring research articles and a note about "corks". The articles are on interesting topics: "Tropicalization and lines on surfaces", "Algebraic structures on symplectic cohomology", and on "Symplectic flexible links". The 29th Gökova Geometry-Topology Conference was partially supported by the Turkish Mathematical Society, Yücelen Group, and "Santori Family Charitable Foundation". Lastly, we want to thank Eylem Zeliha Yıldız for compiling this PGGT volume.
Table of Contents (6 Chapters)
Selman Akbulut, Denis Auroux, and Turgut Önder
tropicalization and lines on surfaces
Mikhail Shkolnikov and Peter Petrov
pp. 1-17
Descent with algebraic structures for symplectic cohomology
Umut Varolgunes
pp. 18-36
Construction of symplectic flexible links
Johan Björklund and Georgios Dimitroglou Rizell
pp. 37-56
Corks
Selman Akbulut
pp. 57-58
Last Pages
Publisher
International Press of Boston, Inc.
Pages 70
Publish Date ISBN-13 Medium Binding Size Publish Status
2025-08-18 978-1-57146-584-9 eBook - - In Print
2025-08-18 978-1-57146-583-2 Print Paperback 7x10 In Print
The International Consortium of Chinese Mathematicians (ICCM) was founded
in 2016, with the purpose of promoting and advancing mathematics within
the extended Chinese community, and building good relationships between
Chinese mathematicians and other mathematicians throughout the world.
The fourth ICCM annual meeting was held in December of 2020 at the University of Science and Technology of China in Anhui.
The present volume consists of 30 expository papers based upon the lectures given by speakers at the event. Consistent with the mission of the Consortium, all contributors were asked to write high-quality expository papers which serve as accessible introductions to — and comprehensive overviews of — the subjects under discussion. All papers have been carefully refereed.
Plenary speakers
Mirror symmetry for double cover Calabi–Yau varieties
Tsung-Ju Lee
pp. 1-21
On free boundary problems in the study of two-body motion
Shuang Miao
pp. 23-54
Cohomology of the moduli of Higgs bundles and the
conjecture
Junliang Shen
pp. 55-72
Motivic Donaldson-Thomas invariant: construction and computation
Yun Shi
pp. 73-86
Stratifications in good reductions of Shimura varieties of abelian type
Chao Zhang
pp. 87-106
Birational classification of varieties in positive characteristic
Lei Zhang
pp. 107-128
Invited speakers
The Gaussian process for particle masses in the near-critical Ising model
Federico Camia, Jianping Jiang, and Charles M. Newman
pp. 129-147
Publisher International Press of Boston, Inc.
Pages 622
Publish Date ISBN-13 Medium Binding Size Publish Status
2025-12-07 978-1-57146-594-8 Print Paperback 7” x 10” In Print
This book explores Teichmüller theory and Grothendieck's dessins d'enfants (a theory of graphs embedded in surfaces) from different angles, covering both the relationship between these two theories and their connections to other geometric topics. It discusses fundamental problems in Riemann surfaces and their moduli theory, complex geometry, and low-dimensional topology, aiming to provide readers with essential reference material on these subjects. The book is suitable for researchers and graduate students in related fields such as low-dimensional topology, combinatorial group theory, complex analysis, and algebraic geometry. It can also serve as a reference for readers interested in the interactions among these fields.
Publisher International Press of Boston, Inc.
Pages 364
Publish Date ISBN-13 Medium Binding Size Publish Status
2026-02-18 978-1-57146-597-9 eBook - - -
2025-12-31 978-1-57146-596-2 Print Paperback 7” x 10” In Print