Format: Hardback, 140 pages, height x width: 235x155 mm, 38 Illustrations, color; 24 Illustrations, black and white
Series: Springer Proceedings in Mathematics & Statistics
Pub. Date: 03-May-2026
ISBN-13: 9783032178091
This volume presents a curated collection of contributions from the Go20 Conference on Scientific Computing and Software, held May 2024, 2024, in Gozo, Malta. Go20 is an exclusive, invitation-only event limited to 20 participants, designed to foster deep exchange among leading experts from academia, industry, and the public sector. With no parallel sessions and 45-minute talks by every attendee, the conference offers an intensive forum for sharing cutting-edge research.
All papers included in this proceedings underwent rigorous peer review. The topics reflect the forefront of scientific computing, emphasizing both theoretical advances and their realization in softwarebridging abstract algorithms with practical implementation. Areas of focus include:
Perturbations and backward error analysis Domain decomposition techniques Superconvergence of non-stiffly accurate implicit RungeKutta methods for index-2 DAEs Parallel-in-time spectral deferred correction and collocation methods Computational approaches for physiological dysfunctions and clinical medicine Parameter estimation for multidimensional stochastic differential equations Novel operator-splitting and fractional-step methods for real and complex PDEs
These contributions advance the rapidly evolving field of scientific computing, addressing challenges with profound societal impactfrom healthcare and medicine to climate modeling and data-driven decision-making. By highlighting the interplay between theory and software, this book serves as a valuable resource for researchers seeking insight into state-of-the-art methods and their practical applications.
Researchers and practitioners in scientific computing, numerical analysis, and applied mathematicsboth academic and non-academicwill find this volume an essential reference for the latest developments in algorithms and software for differential equations and linear systems.
Chapter 1 Structured backward error for the WKB method: Part I: Problems
Without Turning Points.
Chapter 2 Resilience Against Soft Faults through
Adaptivity in Spectral Deferred Correction.
Chapter 3 A Piecewise
Deterministic Approach for Parameter Estimation in Multi-Dimensional
Stochastic Differential Equations.
Chapter 4 Impact of spatial coarsening on
Parareal convergence for the linear advection equation.
Chapter 5 Seven
things I would have liked to know when starting to work on Domain
Decomposition.
Format: Paperback / softback, 172 pages, height x width: 235x155 mm, VI, 172 p.
Series: Lecture Notes in Mathematics
Pub. Date: 26-Apr-2026
ISBN-13: 9783032154125
This book presents a new Lefschetz trace formula for a foliated flow on a compact foliated manifold with a foliation of codimension one. The leaves preserved by the flow and its closed orbits are assumed to be transversely simple. The formula equates two distributions on the real line: one is a renormalized trace of the flows action on two reduced leafwise cohomologies, defined via conormal and dual-conormal currents; the other consists of contributions from the preserved leaves, closed orbits, and a b-trace version of Connes Euler characteristic, defined using a transverse invariant measure on the complement of the preserved leaves. The usual Euler characteristic is undefined here due to non-compactness. The proofs and definitions combine tools from analysis and foliation theory, like small b-calculus, Wittens deformation of differential complexes, heat invariants, and zeta functions of operators, alongside a description of foliations with this type of flow. The exposition is largely self-contained, with prerequisites and references given for further study. The trace formula solves a conjecture of C. Deninger, motivated by his program which links arithmetic zeta functions to foliated geometry. While further generalization is needed for arithmetic applications, the original and technically deep ideas presented here are valuable in themselves and offer a foundation for future work. The book will be of interest to researchers and graduate students in foliation theory, global analysis on manifolds, and arithmetic geometry.
Introduction.- Analytic tools.- Foliation tools.- Foilations with simple
foliated ows.- Conormal leafwise reduced cohomology.- Dual Conormal leafwise
reduced cohomology.- Contribution from M1.- Bibiliography.
Format: Hardback, 376 pages, height x width: 235x155 mm, 3 Illustrations, black and white
Series: Coimbra Mathematical Texts
Pub. Date: 29-Apr-2026
ISBN-13: 9783032137593
This book provides a comprehensive introduction to some key subjects in logic, category theory, algebra and topology. Its five chapters contain the written records of the five courses of the 2022 TACL Summer School (Mira, Portugal, June 14-18, 2022), addressed to graduate students and more experienced mathematicians working in algebra, topology, categories and logic. This volume can help researchers to quickly get into the subject by offering «self-contained» introductions to the subjects.
Chapter 1 Notes on duality theory.
Chapter 2 A Concise and Friendly
Introduction to the Analysis of Algorithms for Continuous Nonlinear
Optimization.
Chapter 3 Remarks on Non-formal Deformation Quantization of
Poisson Manifolds.
Chapter 4 Linear and Nonlinear Fractional PDEs from
Interacting Particle Systems.
Chapter 5 On Bi-Lipschitz Classification of
Real and Complex Singularities.
Format: Hardback, height x width: 235x155 mm, Approx. 350 p.
Pub. Date: 24-May-2026
ISBN-13: 9783032142511
This volume on statistical dependence modeling is published in honor of Claudia Czado and her influential career in statistics. Reflecting the breadth of her research interests, the book presents authoritative peer-reviewed contributions on theoretical foundations, methodological innovations, and applications in dependence modeling, statistical methodology and Bayesian computation. It also features two historical accounts of vine copulas, a field that Claudia Czado has significantly influenced and contributed to. The book serves both as a scholarly resource and as a celebration of her scientific accomplishments.
Preface.- Kjersti Aas, Roger Cooke, Harry Joe, Dorota Kurowicka, Thomas
Nagler Growth cycle of vine copulas.- Nicole Barthel, Dominik Müller, Eike
Brechmann A decade of elevating (with) vine copulas.- Panagiotis Serrano,
Dorota Kurowicka Stochastic simulation inference algorithm in restricted Pair
Copula Bayesian Network with single root node.- Manfred Denker, Aleksey Min
Gibbs copulas.- Harry Joe: Diagnostics for the validity of the simplifying
assumption for vine copulas.- Roger M. Cooke, Tim J. Bedford Identifiability
and the simplifying assumption.- Alexis Derumigny Measures of non
simplifyingness for conditional copulas and vines.- Thomas Nagler, Gerda
Claeskens, Irčne Gijbels On dimension reduction in conditional dependence
models.- Canyi Chen, Ritoban Kundu, Wei Hao, Peter Song Copula structural
equation models for mediation pathway analysis.- Ozan Evkaya, Ariane
Hanebeck, Özge Sahin Clusterspecific ranking and variable importance for
Scottish regional deprivation via vine mixtures.- Ilias Willems, Sara Rutten,
Gilles Crommen, Ingrid van Keilegom: A flexible control function approach for
survival data subject to different types of censoring.- Annette Möller, David
Jobst, Ferdinand Buchner Vine copula based probabilistic weather forecasting
- Review, challenges and future work.- Karoline Bax, Alessandro Fulci, Sandra
Paterlini, Emanuele Taufer Generalized precision matrices for non Gaussian
distributions Theory and portfolio applications.- Matthias Fischer LogTukey
Type distributions as models for operational losses.- Gregor Zens, Sylvia
Frühwirth Schnatter Marginal data augmentation for efficient Bayesian
modeling of counts and rates with a demographic application.
Pages: 284
ISBN: 978-981-98-2571-4 (hardcover)
ISBN: 978-981-98-2681-0 (softcover)
This book provides a clear and accessible introduction to modern algebraic number theory, with a special emphasis on class field theory. Drawing from courses and lectures delivered in seven countries, the text balances simplicity with depth, making advanced topics approachable with minimal reliance on heavy algebraic or analytic machinery.
The book is structured into these distinct chapters; each tailored to a different stage of mathematical training:
Chapter 1 introduces algebraic number fields, progressing at a steady pace with numerous examples — ideal for advanced undergraduates;
Chapter 2 explores complete discrete valuation fields (local fields), a vital area of local algebraic number theory often underrepresented in standard textbooks but crucial in modern research;
Chapter 3 develops abstract class field theory and its applications to both local and global fields, using Neukirch's axiomatic approach to derive fundamental theorems. Extensions to recent developments and generalizations are also discussed.
The final chapter gathers a substantial collection of exercises, designed to test comprehension and guide further exploration. By offering the simplest known pathway to class field theory, this book fills a significant gap left by classic references published decades ago.
Preface
About the Author
Algebraic Number Fields:
Algebraic Prerequisites
Integrality
Dedekind Rings
p-adic Numbers
A Little about Class Field Theory
Complete Discrete Valuation Fields:
Valuation Fields
Discrete Valuation Fields
Completion
Filtrations of Discrete Valuation Fie
Group of Principal Units as Topological ℤp-Module
Set of Multiplicative Representatives
Witt Ring
The Hensel Lemma and Henselian Fields
Extensions of Valuation Fields
Unramified and Ramified Extensions
Galois Extensions and Ramification Groups
Structure Theorems for Complete Discrete Valuation Fields
Cyclic Extensions of Prime Degree
Artin–Schreier Extensions
Hasse–Herbrand Function
Norm and Ramification Groups
Field of Norms
Local Fields with Finite Residue Fields
Class Field Theory:
Main Results of Local Class Field Theory
Neukirch's Abstract Class Field Theory
Local Class Field Theory and Generalisations
Adeles of Global Fields
Zeta Functions and Zeta Integrals
Global Class Field Theory
Exercises:
Algebraic Numbers Exercises
Local Fields Exercises
Class Field Theory and Zeta Functions Exercises
Bibliography
Index
Advanced undergraduates (third year and above) in mathematics. Master's students specializing in number theory or algebra. Doctoral students and postdoctoral researchers in algebraic number theory and related fields. Professors and academic researchers seeking a concise yet modern introduction to class field theory. Mathematicians in related research areas, such as algebra, algebraic geometry, algebraic topology, and mathematical physics, where number theory methods play a role.
Pages: 360
ISBN: 978-981-98-2543-1 (hardcover)
This volume offers a comprehensive exploration of the representation theory of reductive groups over local fields, with emphasis on characters, matrix coefficients, branching laws, and the Weil representation. It brings together a collection of expository lecture notes and original research contributions that highlight both the historical foundations of the subject and the most recent advances in the field.
Designed for graduate students, postdoctoral fellows, and young researchers, the book combines accessible introductions to advanced concepts with state-of-the-art results from leading experts including Anne-Marie Aubert, Roger Howe, and Toshiyuki Kobayashi. It serves both as an entry point to modern representation theory and as a reference for specialists seeking current perspectives.
Originating from the international conference Representations and Characters: Revisiting the Works of Harish-Chandra and André Weil — a satellite event of the Virtual ICM 2022, organized by the Institute for Mathematical Sciences, National University of Singapore, from July 1st to 16th — this volume collects some key research themes from this major meeting and makes them accessible to a wider mathematical audience.
Foreword
Preface
Correspondences between Affine Hecke Algebras and Applications (Anne-Marie Aubert)
Progresses on the Local Gan–Gross–Prasad Conjecture (Cheng Chen)
Symmetry Breaking for PGL(2) over Non-Archimedean Local Fields (Corina Ciobotaru and Jan Frahm)
Invariant Vectors for Depth Zero Supercuspidals of GSp(4) (Jonathan Cohen)
Overview on the Theory of Double Flag Varieties for Symmetric Pairs (Lucas Fresse and Kyo Nishiyama)
On the Local Character Expansions for Principal Series Representations of General Linear Groups (Maxim Gurevich)
Projection of Elliptic Orbits and Branching Laws (Hongyu He)
Mathematics around the Heisenberg Group (Roger Howe)
Proper Actions and Representation Theory (Toshiyuki Kobayashi)
Graduate students, young researchers, and specialists in modern representation theory of reductive groups over local fields.
Pages: 250
ISBN: 978-981-98-2744-2 (hardcover)
This book is devoted to examining a range of results and related research stemming from the following classical theorem: If the center of a group has finite index, then the derived subgroup of the group is finite.
This theorem, long regarded as a cornerstone of group theory, has played a significant role in the development of infinite group theory. The body of work in which it appears is extensive. It has had a profound influence on the field, serving as a catalyst for numerous results and inspiring new approaches to the study of infinite groups. These developments have helped shape the branch of infinite group theory now commonly referred to as the "classical" theory.
Some of the Different Proofs of Schur's Theorem
Some First Generalizations of Schur's Theorem
Central-by-Finite Groups and Virtually Normal Subgroups
Finite-by-Abelian Groups:Restrictions on Conjugacy Classes and One-Generator Normal Closures
Finite-by-Abelian Groups and their Generalizations: X-Conjugacy Classes
Finite-by-Abelian Groups and their Generalizations: X-Conjugate Classes of Subgroups
Schur's Theorem in Linear Groups
Schur's Theorm in Other Algebraic Structures
Graduate students, PhD students, and researchers working in group theory and other branches of algebra. Researchers working in the areas of mathematics and physics employing algebra apparatus.
Pages: 200
ISBN: 978-981-98-2552-3 (hardcover)
ISBN: 978-981-98-2598-1 (softcover)
Revolutions in Mathematics charts the origins and development of key mathematical concepts that have laid the foundation for the advanced technological world we enjoy today. This is a journey through thousands of years of human discovery, effort, and struggle. Behind the simple elegance of everyday mathematics lies a long, winding path filled with false starts, questionable beliefs, rivalries, and persistence in the face of sickness, despair, and doubt.
This book brings those human stories to life, showing how determination and sacrifice shaped the mathematical breakthroughs we now take for granted. At the same time, it offers a clear, accessible understanding of the ideas themselves — designed for the general reader, not the specialist.
By blending history with insight, Revolutions in Mathematics hopes to not only deepen appreciation for the role of mathematics in our world, but also spark curiosity to explore further into mathematics, science, and technology.
Dawn of Mathematics
The Ancient Greeks and Romans
The Birth of our Number System
The Origin and Growth of Algebra
The Foundations of Probability Theory
The Discovery of Calculus
The Development of Group Theory
The Breakthrough of Non-Euclidean Geometry
The Theory of Sets
The Digital Age
This book will appeal to secondary school mathematics or STEM students and teachers. It will also appeal to general readers with an interest in mathematics and the history of science.
Pages: 440
ISBN: 978-981-98-3044-2 (hardcover)
The main subject of this book is singular homology, the simplest of the translations in algebraic topology. In studying this theory and its applications, the book also investigates parts of other disciplines that form its underlying structural layout: homological algebra, homotopy theory, and category theory. The cohomology theories of Alexander–Spanier, Čech, and de Rham are also presented.
This book is an introduction to a complex domain, with references to its advanced parts and ramifications. It is written with minimal prerequisites — basic general topology and little else — and a moderate progression, starting with a very elementary beginning.
A consistent part of the exposition is organised in the form of exercises, with suitable hints and solutions. The book can be used as a textbook for a first course in algebraic topology or for self-study, and also as a reference book for further study.
It is based on a previous version, which has been entirely reviewed, adding several presentations of advanced subjects, and exploring more deeply the interplay of homology and homotopy.
Introduction
Basic elements for Algebraic Topology
Absolute Singular Homology
Computing Singular Homology
Homology and Cohomology Theories
Singular Homology with Coefficients
Universal Coefficients and Products
Fundamental Groupoid and Homotopy Groups
Interactions of Homotopy and Homology
Solutions to the Exercises
Graduate students, PhD students, and researchers in Mathematics.
Pages: 292
ISBN: 978-981-98-2750-3 (hardcover)
This volume offers a systematic introduction to geometric discrepancy theory, rooted in a series of open problems that drive current research. Based on the author's invited talk Results and Problems Old and New in Discrepancy Theory at the Special Semester on Multivariate Algorithms and their Foundations in Number Theory at RICAM, Austria, this book presents the foundational results leading up to these open questions while providing a guided pathway for further investigation.
Designed to be almost self-contained, it requires only basic knowledge of number theory, probability, and analysis. The book emphasizes clarity and accessibility, making it suitable for both beginning graduate students and experienced researchers seeking a structured entry into geometric discrepancy theory.
Introduction
Classical Problem — Dimension 2
Classical Problem — Higher Dimensions
Similar and Homothetic Copies of a Convex Set
Cartesian Products of Sets
Roth Disc Segment Problem
Convex Polygons
Superirregularity
Appendices:
Some Related Topics
A Theorem of Schmidt
Graduate students, researchers and academics in mathematics, particularly those interested in number theory, geometric discrepancy, combinatorics, and multivariate algorithms. It is also a valuable reference for university and research institute libraries.
Pages: 400
ISBN: 978-981-98-2952-1 (hardcover)
This book is designed as a two-semester text. The first semester is devoted to Banach and Hilbert spaces, while the second semester focuses on operator theory.
The book aims not only to present the core concepts in a clear and concise manner, but also to enrich the reader's understanding through numerous illustrations and a wide range of exercise problems. Special focus has been laid on important theorems like open map theorem, closed graph theorem, Hahn-Banach theorems, principle of uniform boundedness, etc, which play a crucial role in the study of functional analysis. Moreover, the reader will also find brief discussions on various tricky topics like comparison between two types of adjoint operators- Hilbert space adjoint and Banach space adjoint, etc. Careful attention has been paid on the hypothesis of the results and counterexamples have been provided for their significance.
The prerequisites for this book include undergraduate courses in real analysis, linear algebra and basic point set topology (for example, metric spaces). Beyond this, some familiarity with measure theory and Lebesgue integration is desirable, but not essential. Most of the use of measure theory and Lebesgue integration occurs in limited ways.
Elements of Analysis
Normed Linear Spaces
Hahn-Banach Theorems and Dual Spaces
Three Fundamental Cornerstones of Functional Analysis
Hilbert Spaces
Operators on Hilbert Spaces
Basic Spectral Properties
Compact Operators
Graduate students, Senior undergraduate students, Researchers interested in functional analysis and operator theory.
Pages: 330
ISBN: 978-981-98-2753-4 (hardcover)
This groundbreaking book is the first comprehensive resource dedicated to the Quadratic Embedding Constant (QEC), the novel numeric invariant that precisely bridges combinatorial graph theory and Euclidean distance geometry. Written by the creator of the QEC, the text presents a systematic and in-depth study of how graphs can be characterized and classified through this invariant, with particular emphasis on its behavior under graph operations such as Star Products and Graph Joins.
Discover how the QEC arises directly from Schoenberg's foundational result — that a graph admits a Quadratic Embedding (QE) if its distance matrix is conditionally negative definite. Learn about the wider significance of QE, which is rooted in Menger's work and appears in harmonic analysis of discrete groups and quantum probability. Furthermore, gain deep insight into distance spectra (distance matrix eigenvalues) and the way the QEC interlaces the largest and second largest eigenvalues.
This self-contained and accessible text is perfect for both non-experts and advanced researchers.
Preface
Graphs and Matrices
Adjacency and Distance Spectra
Quadratic Embedding of Graphs
Quadratic Embedding Constants
Graphs of Diameter Two
Transmission Regular Graphs
Star Products
Paths
Graph Joins
Fan Graphs
Cactus-like Graphs
Miscellaneous Results
Appendix Some Tips for Matrix Analysis
Bibliography
Index
Graduate students and advanced undergraduates in discrete mathematics, combinatorics, and graph theory, as well as postdoctoral researchers and experts interested in applications of finite graphs, especially in network and chemical graph theory. It is essential reading for anyone focused on Graph Theory and its Applications, Spectral Graph Theory, Algebraic Graph Theory, Euclidean Distance Geometry, Chemical Graph Theory. Its self-contained and step-by-step presentation makes it friendly for non-experts.