Book
Nov 2025
Winner of the 2025 Ferran Sunyer i Balaguer Prize
Provides the first systematic and unified treatment of set-theoretic solutions to the Yang-Baxter equation
Bridges foundational theory and current research in the area
Part of the book series: Progress in Mathematics (PM, volume 361)
This monograph provides the first comprehensive introduction to set-theoretic solutions of the Yang–Baxter equation and their deep connections with skew braces. In recent decades, set-theoretic solutions have emerged as an accessible yet rich domain of study, offering new algebraic structures and revealing unexpected connections between seemingly distant fields. A key breakthrough in this direction was the discovery of braces by Rump and the later generalization to skew braces, which provide an elegant algebraic framework for understanding and constructing set-theoretic solutions. This book offers a self-contained, structured, and pedagogically motivated treatment of the subject. Each chapter ends with a list of exercises to work on the presented topics, some open problems, and comments on the authorship and development of the results presented.
The primary audience consists of researchers and advanced graduate students working on or entering topics related to the Yang–Baxter equation, especially those with interests in algebra, set-theoretic solutions, and skew braces theory. Given its self-contained nature, the book is also suitable for graduate students seeking a pathway into current research, as it provides foundational material alongside recent developments.
Conference proceedings
Sep 2025
Covers topics ranging from physics to health, complex networks, and human behavior in economics
Serves as a platform for the exchange of ideas and discussions on the latest trends in these fields
Convenes contributions by experts from all over the world
Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 514)
This volume gathers selected papers presented at the IC-MSQUARE 2024 - 13th International Conference on Mathematical Modeling in Physical Sciences held in Kalamata, Greece from September 30–October 3, 2024. This proceedings volume offers a compilation of cutting-edge research, which aims to advance the knowledge and development of high-quality research in mathematical fields related to physics, chemistry, biology, medicine, economics, environmental sciences, and more.
Annually held since 2012, the IC-MSQUARE conference serves as a platform for the exchange of ideas and discussions on the latest technological trends in these fields. This book is an invaluable resource for researchers, academicians, and professionals in these areas seeking to stay up-to-date with the latest developments in mathematical modeling.
Book
Nov 2025
Provides an explicit presentation of several different models in Celestial Mechanics
Offers a comprehensive overview of various problems in Celestial Mechanics and Astrodynamics
Presents models in the conservative setting and also in the dissipative framework
Part of the book series: Springer Monographs in Mathematics (SMM)
This book is devoted to the presentation and discussion of some models of relevance in Celestial Mechanics and Astrodynamics. The motions of celestial bodies, either natural or artificial, are governed by conservative forces, like the gravitational attraction that preserve the total energy and by dissipative forces, like the tidal torque, Stokes drag, and the Poynting-Robertson effect. The basic idea of this book is to describe in each chapter a model in the conservative setting, providing its main features, and then to extend the model by including dissipative forces. In fact, the dynamics of many objects of the Solar system is well described, in a first approximation, by a conservative model; however, in the long term, dissipative effects may play a relevant role, for example, in shaping the dynamics and affecting the evolutionary history of the Solar system.
Motivated by this observation, in this book, different models are presented and their main features are described in the conservative setting, but dissipative contributions, pertinent to the model, are added as well, which may lead to a completely different dynamics on long time scales. Conservative systems have a larger variety of motions, e.g., the dynamics can take place on rotational tori, librational motions, periodic orbits, and chaotic trajectories. On the contrary, dissipative systems admit a less rich dynamics, since the dissipation forces the motion to take place on a few attractors, e.g., rotational tori, periodic orbits or strange attractors. Besides, dissipative systems often need extra parameters to compensate for the loss of energy and to allow the dynamics to take place on non-trivial attractors.
The book is addressed to graduate students and researchers interested in models of Celestial Mechanics and Astrodynamics.
Book
Oct 2025
Presents in-depth and accessible surveys of topics in singularity theory, including connections with other subjects
Ideal for graduate students and newcomers to the area, and as a reference for specialists
Encourages readers to go deeper into the subject by offering illuminating insights and useful bibliographies
This is the eight volume of the Handbook of Geometry and Topology of Singularities, a series that provides an accessible account of the state of the art of the subject, its frontiers and its interactions with other areas of research.
This volume consists of twelve chapters with reader-friendly introductions to several important topics and aspects of singularity theory, such as:
Plane curve singularities studied by means of divides, which capture a lot of their topology.
Viro’s method to study the topology of real algebraic varieties, providing a wide range of possible combinations of topological and combinatorial invariants.
Local tropicalization, a technique for attaching a combinatorial object to germs of subvarieties of algebraic tori and toric varieties.
The theory of Zariski pairs and superisolated singularities.
The McKay correspondence, a deep connection that links group theory, algebraic geometry, and representation theory.
Calculations with Characteristic Cycles, a deep concept in the interplay between algebraic geometry, representation theory and microlocal analysis.
The monodromy zeta functions in singularity theory.
The singularities of the minimal model program of complex quasi-projective varieties.
A general theory of Thom polynomials associated to the classification of map-germs.
A discussion on indices and residues, intertwining the theories of complex analytic singular varieties and singular holomorphic foliations.
The Monodromy in Integral Geometry and PDE.
The topological theory of Hyperplane Arrangements.
The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.
Book
Open Access
Oct 2025
You have full access to this open access Book
This book is open access, which means that you have free and unlimited access
Self-contained introduction to SPDEs with space-time white noise, using the random field approach
Covers the basic topics of the theory of SPDEs and gives an introduction to some fundamental topics in the field
Provides a good background to begin research in the area
Part of the book series: Springer Monographs in Mathematics (SMM)
This open access book provides a comprehensive introduction to the theory of stochastic partial differential equations (SPDEs). The focus is on SPDEs driven by Gaussian space-time white noise. The book covers both linear and nonlinear SPDEs, with Lipschitz and locally Lipschitz coefficients and multiplicative noise. It provides a modern presentation of the theory of stochastic integration with respect to space-time white noise and unifies many results in the literature. The book discusses fundamental topics such as existence and uniqueness of random field solutions, along with their space-time sample path regularity properties. The book also presents a selection of additional topics such as weak solutions in law to SPDEs, space-time Markov properties, asymptotic bounds on moments, comparison theorems, a study of polarity of points for SPDEs with additive noise, and a study of SPDEs with rough initial conditions that includes the parabolic and hyperbolic Anderson models and their intermittency properties. In the context of the stochastic heat equation, the book discusses additional important topics including invariant and limit measures, reversible measures and their relationship to bridge measures, irreducibility properties, and large interval asymptotics. The appendices gather results from analysis and stochastic processes that are used throughout the core of the book, including key elements from the general theory of stochastic processes, a detailed presentation of Kolmogorov’s anisotropic continuity criterion, numerous integrability properties of the fundamental solutions and Green's functions associated to the heat and wave partial differential operators, explicit calculations of some space-time convolution series and some useful Gronwall-type lemmas. The book aims to be a reference for established researchers in the field of SPDEs, as well as for those who are interested in entering the field and becoming familiar with its techniques. In particular, graduate and postgraduate students with a background in stochastic analysis will find here a comprehensive and self-contained source of information which provides essential expertise in the subject.
Book
Nov 2025
Contributions on the state-of-the art on the problems studied
Survey articles (apart from research papers) included in the volume
The domains investigated are of current interest and it is expected that the volume will reach wide readership
This book offers a comprehensive exploration of cutting-edge research in Analytic Number Theory, celebrating the profound contributions of Helmut Maier on his 70th birthday. With chapters penned by leading mathematicians from around the globe, this volume presents state-of-the-art findings and insights into a wide array of topics within the field.
Readers will encounter in-depth studies on subjects such as random matrix models for cusp forms, the Chevalley-Bass theorem, and Weierstrass Fractal Drums. The book also delves into the $L_q$ norm of Rudin-Shapiro polynomials, shifted-prime divisors, and sharp local estimates for smooth numbers. Further, it examines the invariants of $L$-functions, an analogue of the Mertens function, the Riemann Hypothesis zeta function, Dirichlet polynomials and exponential sums.
This collection is an invaluable resource for graduate students and seasoned researchers in Analytic Number Theory and related disciplines. It not only honors Maier's groundbreaking work but also serves as a beacon for future research, offering insights and methodologies that will inspire continued exploration and discovery in the field.
Conference proceedings
Nov 2025
Offers a comprehensive and interdisciplinary approach to the latest advancements in PDEs
Bridges the gap between theoretical research and its applications
Provides cutting-edge insights that are not available in other publications
Part of the book series: ICIAM2023 Springer Series (ICIAMSS, volume 5)
This book presents the proceedings of the Minisymposium “Various Methods for the Analysis of PDEs” held at the International Congress on Industrial and Applied Mathematics (ICIAM) 2023. This volume brings together a diverse group of researchers, practitioners, and experts who have shared their latest developments and innovations in the field of Partial Differential Equations (PDEs).
The papers included in this volume reflect the high quality and breadth of research presented at the session. Covering a wide range of topics, this collection showcases the dynamic and interdisciplinary nature of the Analysis of PDEs. Each contribution has undergone a rigorous peer-review process to ensure the highest standards of academic excellence.
Interpolation Inequalities: Novel contributions to the field, including stability results for the Sobolev inequality and the Gaussian logarithmic Sobolev inequality with explicit and dimensionally sharp constants.
Strichartz Estimates: New estimates specifically for orthonormal families of initial data, extending traditional Strichartz estimates to provide deeper insights into the behavior of solutions to dispersive equations, including the wave equation, Klein-Gordon equation, and fractional Schrödinger equations.
Asymptotic Behavior: Detailed analysis of the asymptotic behavior for the massive Maxwell–Klein–Gordon system under the Lorenz gauge condition in dimension (1+4), including scattering results.
Time-Dependent Free Schrödinger Operator: A new characterization of this operator, highlighting its unique invariance under the Galilei group in Euclidean space-time.
Lifespan Estimates: Analysis of the lifespan of solutions to the damped wave equation, with decay estimates for particular initial data in the case of nonlinearity with subcritical Fujita exponent.
This book aims to provide readers with a profound and cohesive understanding of the current state of splitting optimization while inspiring future research and innovation in this dynamic field.
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