Format: Paperback / softback, height x width: 235x155 mm, 13 Illustrations, black and white
Series: Universitext
Pub. Date: 25-Jun-2026
ISBN-13: 9783032199096
This textbook provides a concise introduction to complex analysis, analytic functions, and Riemann surfaces, along with several more recent developments motivated by the theory of several complex variables.
The first two chapters present classical material: the basic properties of analytic functions, complex integration and residue calculus, the Riemann Mapping Theorem, and the theory of harmonic functions. The theory of elliptic functions is introduced and used to prove Montels theorem on the universal cover of the twicepunctured plane. This result becomes a key tool in the classical theory of complex dynamics developed in the book. As another application of complex analysis, the text includes selected results from analytic number theory, in particular the prime number theorem and a reformulation of the Riemann Hypothesis in terms of the distribution of prime numbers.
Potential theory is introduced in the following chapter and later becomes the central tool for developing the theory of Riemann surfaces, whose main result is the uniformization theorem. The final chapter presents methods from the theory of several complex variables. A key result here is Hƶrmanders L2-estimate for the -operator, which is applied to solve the Beltrami equation. The chapter also includes a quantitative version of Carlesons theorem characterizing domains with nontrivial Bergman spaces, giving an optimal lower bound (conjectured by Suita) for the Bergman kernel in terms of logarithmic capacity.
Based on courses taught over many years, the material in this book has been refined for decades and the presentation is intentionally succinct, favoring the simplest available proofs. This approach makes it possible to include material that would typically require two separate volumes. Each chapter concludes with a collection of exercises ranging from standard problems to more advanced ones.
Chapter 1. Local Properties of Holomorphic Functions.
Chapter 2. Singularities, Residues, Conformal Maps.
Chapter 3. Further Properties of Holomorphic Functions.
Chapter 4. Some Applications of Complex Analysis.-
Chapter 5. Potential Theory.
Chapter 6. Riemann Surfaces.
Chapter 7. š¯‘³2-theory for the š¯¯¸-equation.
Format: Hardback, 161 pages, height x width: 235x155 mm, II, 161 p.
Series: Simons Symposia
Pub. Date: 08-Jun-2026
ISBN-13: 9783032180063
This proceedings volume contains articles related to the research presented at the 2022 Simons Symposium on p-adic Hodge theory. This symposium was focused on recent developments in p-adic Hodge theory and applications to related fields including number theory and algebraic geometry. This volume contains articles on some of these new developments in this rapidly evolving field and other research that arose from the symposium.
Chapter 1 v-vector bundles on p-adic fields and Sen theory via the HodgeTate stack.
Chapter 2 The analytic topology suffices for the B+dR-Grassmannian.
Chapter 3 Vanishing of cohomology in infinitely ramified towers.
Chapter 4 Monodromy representations of p-adic differential equationsin Families.
Chapter 5 Point objects on abelian varieties.
Chapter 6 Somefoundational results in p-adic geometry.
Format: Hardback, 376 pages, height x width: 240x168 mm, XII, 376 p.
Series: Synthesis Lectures on Mathematics & Statistics
Pub. Date: 11-Jun-2026
ISBN-13: 9783032220110
This book discusses long memory and long range dependence for continuous time financial models. While traditional models are Markovian, which have short memory, models with long memory have not been focused on and only studied in the discrete time series modeling context. The development of increasingly complex financial models products requires the use of advanced mathematical and statistical methods. Though the mathematics behind these models are more complicated, these models are more practical from the perspectives of finance, biology, and physics. The author presents models driven by non-Gaussian fractional Levy processes, which are more useful models in these fields. In addition, the author incorporates long memory into the model by using noise driven by fractional Brownian motion, which is neither a semi martingale nor a Markov process, except the one half Hurst parameter case, where it is Brownian motion. Fractional stochastic differential equations are state-of-the art in continuous time asset pricing and interest rate models. Though pricing has been studied, parameter estimation has not been well studied. Readers will learn advanced mathematical and statistical methods in finance, and special attention is paid to stylized facts such as high dimensional models and data, models with jumps, and models with long-memory.
Berry-Esseen Bound for the Least Squares Estimator in the Fractional
Ornstein-Uhlenbeck Process.- Large Deviations in Testing Fractional
Ornstein-Uhlenbeck Models.- Minimum Contrast Estimation in Fractional
Ornstein-Uhlenbeck Process.- Hypotheses Testing in Nonergodic Fractional
Ornstein-Uhlenbeck Models.- Nonparametric Estimation in Heath-Jarrow-Morton
Term Structure Models Driven by Fractional Levy Processes.- Bootstrap
Confidence Interval for Fractional Diffusions and American Options.
Format: Hardback, 185 pages, height x width: 240x168 mm, VIII, 185 p.
Series: Synthesis Lectures on Mathematics & Statistics
Pub. Date: 03-Jun-2026
ISBN-13: 9783032209139
This book provides essential theoretical tools for stochastic modeling. This Second Edition includes expanded discussion of the most used models in applications such as Markov chains with discrete-time parameters, hidden Markov chains, Poisson processes, and birth and death processes. The authors have also added new topics, including semi-Markov processes, marked Poisson processes, Hawkes processes, time reversibility and detailed balance in continuous-time Markov chains, and age-dependent branching processes. The book includes updated examples, simulation methods, and applications to complement those presented in the first edition. This book is concise and rigorous, presenting the material in an easily accessible manner that allows readers to learn how to address and solve problems of a stochastic nature.
Discrete-Time Markov Chain.- Poisson Processes and its Extensions.-
Continuous-Time Markov Chain Modeling.- Branching Processes.- Hidden Markov
Model.
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Format: Hardback, 192 pages, height x width: 235x155 mm, VIII, 192 p.
Series: Advances in Mathematical Fluid Mechanics
Pub. Date: 29-Jun-2026
ISBN-13: 9783032210937
This book explores state-of-the-art developments in theoretical and applied fluid mechanics with a focus on stochastics and their role in mathematical analysis and numerical simulation of different types of flows. Chapters are based on lectures given at the summer school Stochastics in Fluids, held in Prague in August 2023. With its accessible and flexible presentation, readers will be motivated to deepen their understanding of how mathematics and physics are connected. Specific topics covered include:
Stochastic Lagrangian theory of zonal flows Stochastic models in turbulence Turbulent flows and stochastic modeling Small noise inviscid limit
This book appeals to graduate students and researchers in both mathematics and physics.
Stochastic modelling of small turbulent scales.- Invariant measures in
the small noise inviscid limit.- Stochastic models in turbulence.- Turbulent
flows: Lagrangian stochastic modelling.- Stochastic modeling of acceleration
in the under-resolved turbulent flows; applications to two-phase flows.
Format: Hardback, 183 pages, height x width: 235x155 mm, 30 Illustrations, color; 6 Illustrations, black and white
Series: ICIAM2023 Springer Series
Pub. Date: 17-Jun-2026
ISBN-13: 9789819573097
This book presents the proceedings of two minisymposiaDelay and Stochastic Differential Equations in Life Sciences and Engineering and Stochastic Modelling in Financeheld at the International Congress on Industrial and Applied Mathematics (ICIAM) 2023 in Tokyo, Japan. It brings together a diverse collection of theoretical and applied research in delay and stochastic differential equations (DDEs and SDEs), showcasing the depth and breadth of current developments in these areas.
The papers included in this book reflect the high quality and versatility of research presented at the sessions. Covering a wide range of topics, they collectively illustrate the richness of delay and stochasticity as drivers of complex dynamical behavior. Each contribution has undergone a rigorous peer-review process to ensure the highest standards of publication.
Key topics include delay and resonance, periodic solutions, numerical methods for SDEs, CesÄ…ro limits for Volterra convolution equations, stochastic modeling and big data in finance, incomplete market analysis, deterministic and stochastic pantograph equations.
This book aims to provide readers with a cohesive and insightful overview of current research in DDEs and SDEs, while inspiring future innovations and applications across disciplinesfrom physics and biology to financial engineering.
Delay and resonance: from differential equations to random walks.-
Periodic solutions of a delay differential equation with a periodic
multiplier.- Adaptive mesh construction for the numerical solution of
stochastic differential equations with Markovian Switching.- Solution space
characterisation of perturbed linear functional and integro-differential
Volterra convolution equations: Cesaro limits.- Stochastic Modelling and
Applications of Big Data in Finance.- Incomplete market analysis of optimal
consumption and robust portfolio for the 4/2 stochastic volatility model.-
Characterisation of asymptotic behaviour of perturbed deterministic and
stochastic pantograph equations.
Format: Paperback / softback, 189 pages, height x width: 235x155 mm, V, 189 p.
Series: Lecture Notes in Mathematics
Pub. Date: 12-Jun-2026
ISBN-13: 9783032205704
This book provides an introduction to the new field of -geometry and its applications to the construction of certain quotient spaces that cannot be approached within usual algebraic geometry, specifically quotients of Siegel moduli spaces by the action of Hecke correspondences. -geometry is a geometry obtained from usual algebraic geometry by adjoining a Fermat quotient operator; the latter morally plays the role of an arithmetic differentiation with respect to a prime integer. The book assumes some basic knowledge of the algebraic geometry of schemes, including abelian schemes, but it is otherwise self-contained.
Its intended audience includes mathematics graduate students and researchers interested in algebraic geometry and number theory.
Chapter 1. Introduction.
Chapter 2. Main concepts and results.
Chapter 3. Proofs of the main results.
Chapter 4. Background and required results in GIT.
Format: Hardback, 216 pages, height x width: 235x155 mm, XII, 216 p.
Series: Nonlinear Physical Science
Pub. Date: 03-Jun-2026
ISBN-13: 9789819582907
This book will present a comprehensive exploration of the geometric bifurcation theory (GBT), a novel approach that employs information geometry to analyze dynamical systems. It will delve into the mathematical foundations of GBT, including the Riemannian metrical structure of parameter spaces, Fisher information metric, scalar curvature, and their application to local and global bifurcations. The book will cover the limitations of classical bifurcation theory (CBT) and demonstrate how GBT overcomes these by providing a more complete characterization of stability and addressing the global behavior of nonlinear dynamical systems. Specific topics will include the geometric interpretation of bifurcations, stability analysis using curvature scalar, scaling analysis using Fisher information, and the application of GBT to study complex and nonlinear phenomena, especially where the standard methods show little or no solution.
Introduction.- ScalingPropertiesNearLocalBifurcations.-
BifurcationsinTwo-dimensionalSystems.- TheGeometricBifurcationTheory.