Tomoyuki Miyaji, Shin-Ichiro Ei, & Masayasu Mimura (Deceased)

A Billiard Problem in Nonlinear Dissipative Systems

Details
Explanations & Abstract

In classical physics, a billiard problem explores the trajectory of an idealized particle or disk bouncing elastically off rigid boundaries within a closed domain, governed almost entirely by geometry and conservation laws. This book steps into complex nonlinear physics by introducing nonlinear dissipative systems into the equation.

The text centers on self-propelled or localized systems (such as self-propelling rigid disks, pulses, or traveling waves) moving through an environment where energy is continually input and dissipated. Unlike traditional billiard systems where incoming and outgoing angles are strictly equal, the trajectory of a billiard disk in a nonlinear dissipative system is heavily dictated by its own inherent, internal dynamics and localized instabilities upon wall interactions.

The authors utilize center-manifold reductions, bifurcation theory, and numerical tracking methods to show how complex, autonomous boundary reflections emerge from reaction-diffusion and pattern formation frameworks.

️ Table of Contents

While the complete subsection layout remains under publisher finalization for its upcoming release, the primary structure focuses on:

  1. Introduction to Classical vs. Dissipative Billiards

  2. Self-Propelled Particles and Localized Patterns

  3. The Dynamics of a Self-Propelling Rigid Disk near a Boundary

  4. Asymptotic Reflection and Interaction Principles

  5. Bifurcation Analysis of Boundary Collisions

  6. Applications to Reaction-Diffusion Systems

  7. Numerical Experiments and Conclusions

    P.N. Natarajan

    An eminent mathematician and former Professor and Head of the Department of Mathematics at Ramakrishna Mission Vivekananda College, Chennai, India. He has published extensively in the fields of ultrametric analysis and classical summability theory.

    An Introduction to Ultrametric Summability Theory (3rd Edition)

    Details
    Explanations & Abstract

    This book presents a thorough survey of ultrametric summability theory, which is an advanced intersection of a classical branch of mathematics (summability theory) and a modern area of abstract analysis (ultrametric, or non-Archimedean, analysis).

    In traditional calculus and analysis, sequences and series are evaluated over real ($\mathbb{R}$) or complex ($\mathbb{C}$) fields. This text shifts the domain to a complete, non-trivially valued, ultrametric field $K$ (such as the $p$-adic field $\mathbb{Q}_p$). Because ultrametric fields lack standard geometric ordering and classical convexity, many traditional theorems break down (e.g., the standard Hahn-Banach theorem fails).

    The author systematically details how classic matrix transformation methods—such as the Nörlund, Weighted Mean, Euler, and Taylor methods—behave under an ultrametric topology. The 3rd Edition is fully updated and introduces three entirely new chapters dedicated to sequence spaces and summability matrices, reflecting the latest research developments in the field.

    ️ Table of Contents

    Based on the foundational chapters of the theory and the newly expanded 3rd edition structure:

    1. Introduction and Preliminaries

    2. Some Arithmetic and Analysis in $\mathbb{Q}_p$; Derivatives in Ultrametric Analysis

    3. Ultrametric Functional Analysis

    4. Ultrametric Summability Theory

    5. The Nörlund and The Weighted Mean Methods

    6. The Euler and The Taylor Methods

    7. Tauberian Theorems

    8. Silverman–Toeplitz Theorem for Double Sequences and Double Series

    9. The Nörlund Method and The Weighted Mean Method for Double Sequences

    10. Sequence Spaces in Ultrametric Fields (New for 3rd Edition)

    11. Advanced Matrix Transformations and Summability Matrices (New for 3rd Edition)

    12. Recent Developments and Applications in Ultrametric Spaces (New for 3rd Edition)




Leonid Positselski

A prominent research mathematician at the Institute of Mathematics, Czech Academy of Sciences. He is highly recognized for his foundational work in homological algebra, semi-infinite homological algebra, and algebraic geometry.

Contraherent Cosheaves on Schemes

Details

  • Publisher: Birkhäuser (an imprint of Springer Nature)

  • Publication Date: Expected June/September 2026

  • Format: Hardcover (approx. 515 pages)

  • Language: English

  • ISBN-13: 978-3-032-26444-2 (9783032264442)

  • ISBN-10: 3032264448

  • Subject Categories: Algebraic Geometry, Homological Algebra, Category Theory

Explanations & Abstract

The subject of this comprehensive monograph lies on the strict frontier where abstract algebraic geometry meets modern homological algebra.

While quasi-coherent sheaves are standard, universally utilized building blocks in algebraic geometry (acting as the localized equivalent of modules over a ring), their dual counterparts—cosheaves—have historically lacked a widely accepted, well-behaved analogue for general scheme theory.

This volume introduces, details, and develops the theory of contraherent cosheaves. Contraherent cosheaves serve as the proper dual to quasi-coherent sheaves, providing a robust, globalized algebraic framework for cotorsion and contraadjusted modules across various geometric environments. The text heavily explores their interactions with derived and contraderived categories on quasi-compact semi-separated schemes, offering deeper homological tools for algebraic geometers tackling complex, global problems.

️ Table of Contents
 

  1. Introduction  

  2. Contraadjusted and Cotorsion Modules  

  3. Contraherent Cosheaves over a Scheme  

  4. Locally Contraherent Cosheaves  

  5. Derived Categories on Quasi-Compact Semi-Separated Schemes  

  6. Becker's Contraderived Categories on Quasi-Compact Semi-Separated Schemes  

  7. Noetherian Schemes  

  8. Morphisms of Finite Type Between Noetherian Schemes  

    Steen Thorbjørnsen

    An Associate Professor at Aarhus University, Denmark. He is an established researcher specializing in free probability theory, random matrices, operator algebras, and advanced measure/integration frameworks.

    Measure and Integration:
    An Introductory Path Toward Functional Analysis and Probability

    Details

    • Publisher: Birkhäuser (an imprint of Springer Nature)

    • Publication Date: Expected July 2026

    • Series: Cornerstones

    • Format: Hardcover (approx. 574–600 pages)

    • Language: English

    • ISBN-13: 978-3-032-24663-9 (9783032246639)

    • ISBN-10: 3032246636

    • Subject Categories: Mathematical Analysis, Functional Analysis, Probability Theory & Stochastic Processes

    Explanations & Abstract

    This text is a comprehensive, modern textbook designed to provide students with a rigorous foundation in classical measure and integration theory. Rather than treating measure theory as an isolated, abstract discipline, the book serves as an intentional gateway ("an introductory path") to the two major fields that rely on it: Functional Analysis and Probability Theory.

    The volume bridges the gap between elementary real analysis and graduate-level mathematics. It guides the reader through structural foundations—from $\sigma$-algebras and abstract measures to Lebesgue integration, $L^p$ spaces, and convergence theorems. Because the author is an active researcher in probability and operator theory, the text naturally emphasizes themes and problem sets that reappear in advanced stochastic calculus, Hilbert space theory, and modern probability frameworks.

    ️ Table of Contents

    While the detailed sub-chapter outline remains under final publisher embargo for its July 2026 release, the textbook adheres to the classic "Cornerstones" mathematical architecture:

    1. Introduction and Motivation

    2. $\sigma$-Algebras and General Measures

    3. Construction of Measures (Outer Measures and Carathéodory's Theorem)

    4. Lebesgue Measure on $\mathbb{R}^n$

    5. Measurable Functions

    6. The Abstract Lebesgue Integral

    7. Convergence Theorems (Monotone Convergence, Dominated Convergence, Fatou's Lemma)

    8. Product Measures and Fubini’s Theorem

    9. $L^p$ Spaces and Classical Inequalities

    10. Signed and Complex Measures (Radon-Nikodym Theorem)

    11. Foundations for Functional Analysis (Hilbert and Banach Spaces)

    12. Foundations for Probability Theory (Independence, Random Variables, and Laws of Large Numbers)

      Loring W. Tu

      A distinguished mathematician and Professor of Mathematics at Tufts University. He is a co-author of the classic textbook Differential Forms in Algebraic Topology alongside his late advisor, Raoul Bott.

      An Introduction to Manifolds (3rd Edition)

      Details

      • Publisher: Springer-Verlag New York Inc.

      • Publication Date: Expected June 2026

      • Series: Universitext

      • Edition: 3rd Edition (Completely revised and updated)

      • Format: Paperback (approx. 436 pages)

      • Language: English

      • ISBN-13: 978-1071653364 (9781071653364)

      • ISBN-10: 1071653369

      • Subject Categories: Differential Geometry, Topology, Mathematical Analysis

      Explanations & Abstract

      Smooth manifolds—the higher-dimensional analogues of smooth curves and surfaces—are fundamental building blocks in modern geometry, theoretical physics, and advanced data analysis. This widely acclaimed textbook provides a streamlined introduction to the theory of manifolds, deliberately structured to help advanced undergraduate and graduate students achieve rapid mastery of the essentials.

      By the conclusion of the text, readers gain the mathematical capacity to calculate one of the most basic topological invariants of a manifold: its de Rham cohomology.

      The 3rd Edition places a heavy emphasis on structural clarity and simplification. While maintaining the overall structural architecture of the previous editions, every single section has been meticulously rewritten. It introduces brand new or significantly simplified proofs, sharper explanations, and a wider variety of exercises with accompanying hints and solutions.

      ️ Table of Contents

      • Preface to the Third Edition

      • Preface to the Second Edition  

      • Preface to the First Edition  

      • Chapter 1: Euclidean Spaces  

      • Chapter 2: Manifolds  

      • Chapter 3: The Tangent Space  

      • Chapter 4: Lie Groups and Lie Algebras  

      • Chapter 5: Differential Forms  

      • Chapter 6: Integration  

      • Chapter 7: De Rham Theory  

      • Appendices  

        • A. Point-Set Topology  

        • B. The Inverse Function Theorem on and Related Results  

        • C. Existence of a Partition of Unity in General  

        • D. Linear Algebra  

        • E. Quaternions and the Symplectic Group  

      • Solutions to Selected Exercises  

      • Hints and Solutions to Selected End-of-Section Problems  

      • List of Symbols  

      • References  

      • Index  

        Sandro Zagatti, Maria Teresa Rotolo, & Antonio Lerario

        Functional Analysis

        Details

        • Publisher: Springer Nature Switzerland / Springer International Publishing

        • Publication Date: Expected June/July 2026

        • Series: SISSA Springer Series (Volume 7)

        • Format: Hardcover (approx. 133–150 pages)

        • Language: English

        • ISBN-13: 978-3-032-24474-1 (9783032244741)

        • ISBN-10: 3032244749

        • Subject Categories: Mathematics, Mathematical Analysis, Functional Analysis

        Explanations & Abstract

        This textbook is an introductory, mathematically rigorous volume based on personal lecture notes compiled from the Functional Analysis course taught for many years at SISSA (the International School for Advanced Studies).

        Designed primarily for upper undergraduate and early graduate students transitioning into advanced research, the text focuses heavily on providing smooth, detailed proofs for core topological and functional-analytic principles. Rather than overwhelming the reader with exhaustive catalogs of niche operators, the book carefully isolates the fundamental tools necessary to explore differential equations, geometry, and advanced real analysis. It serves as an optimal companion for self-study and foundational university lectures.

        ️ Table of Contents

        While the complete internal layout is under publisher finalization for its upcoming release, the curriculum structures itself around the core pillars of the SISSA syllabus:

        1. Introduction and Topological Prerequisites

        2. Normed and Banach Spaces

        3. Hilbert Spaces and Geometry of Inner Products

        4. The Hahn-Banach Theorem and Core Extensions

        5. Baire Category Theorem and Fundamental Principles (Open Mapping and Closed Graph Theorems)

        6. Dual Spaces and Weak Topologies

        7. Bounded Linear Operators and Boundedness Principles

        8. Introduction to Compact Operators and Spectral Theory




Andreas Demleitner

The Classification of Hyperelliptic Groups in Dimension 4

Details
Explanations & Abstract

This monograph explores the geometry of hyperelliptic manifolds, which represent a higher-dimensional generalization of classical hyperelliptic surfaces. Historically classified by Enriques, Severi, and Bagnera-de Franchis, traditional hyperelliptic surfaces are compact complex surfaces characterized by a Kodaira dimension of zero, geometric genus of zero, and irregularity of one.

This text expands these classical ideas to complex tori of arbitrary dimension by quotienting them by finite groups acting freely and without translations. The book's primary focus is providing a complete classification of hyperelliptic manifolds in dimension four—a major milestone that had previously remained unexplored.

By combining techniques from group theory, representation theory, and computer algebra systems (specifically utilizing GAP), the author successfully identifies all finite groups that admit free and translation-free actions on four-dimensional complex tori. Furthermore, the text investigates the torsion order of the canonical divisor for hyperelliptic manifolds in dimensions up to five and highlights deep connections with Iitaka’s conjecture and complex Bieberbach groups.

️ Table of Contents

While the detailed subsection layout is under publisher finalization for its upcoming release, the core architectural chapters of the monograph include:

  1. Introduction and Historical Background

  2. Foundations of Hyperelliptic Manifolds and Complex Tori

  3. Group Actions and Representation Theory Frameworks

  4. Computational Methods using the GAP System

  5. The Classification of Hyperelliptic Groups in Dimension 4

  6. The Torsion Order of the Canonical Divisor in Dimensions $\le 5$

  7. Connections to Iitaka’s Conjecture and Complex Bieberbach Groups

  8. Summary and Future Research Outlines


    Kacha Dzhaparidze

    De Branges' Theory for Processes with Stationary Increments

    Details
    Explanations & Abstract

    This highly specialized volume bridges a fundamental gap between advanced function theory and probability. It focuses on the application of Louis de Branges' theory of entire functions—specifically Hilbert spaces of entire functions—to the structural behavior of stochastic processes with stationary increments.

    Traditional studies of stationary increments rely on standard spectral representations. This work instead leverages de Branges matrix-valued functions and canonical differential systems to study underlying operators, moving average representations, and structural expansions (such as the Karhunen–Loève expansion). The monograph provides essential reading for advanced researchers and graduate students seeking deep geometric and analytic tools within probability theory and complex analysis.

    ️ Table of Contents

    Part I. Functions on a Half-Plane

    Part II. De Branges Spaces of Entire Functions

    Part III. Stochastic Processes with Stationary Increments