Complex Geometry and Mathematical Physics:
Lorentzian Geometry and Field Equations (Book III-A)

DETAILS
EXPLANATIONS

This volume is the first part (Book III-A) of a broader project exploring the interaction between differential geometry, complex geometry, general relativity, and mathematical physics. The book focuses on Lorentzian geometry and the mathematical foundations of gravitational field theories. Topics include spacetime causality, Lorentzian submanifolds, compact Lorentzian holonomy, Maxwell's equations, Einstein's field equations, geodesic motion, gravitational effects in classical and quantum settings, and applications of modern geometric methods to physics. The authors emphasize how geometric structures provide a natural language for describing physical laws and spacetime phenomena.

TABLE OF CONTENTS

The complete chapter-by-chapter table of contents was not available in the publicly accessible bibliographic sources consulted. However, the book description indicates coverage of the following major themes:

  1. Lorentzian Geometry
  2. Causality Theory of Spacetimes
  3. Submanifolds of Lorentzian Manifolds
  4. Compact Lorentzian Holonomy
  5. Maxwell's Equations and Geometric Structures
  6. Geodesic Motion and Newtonian Limits
  7. Kepler's Problem and Mercury's Perihelion Shift
  8. Morse Theory for Light Rays
  9. Quantum Aspects of Gravitation
  10. Bending of Light in Quantum Gravity
  11. Einstein's Linearized Field Equations
  12. Field Equations in Vacuum and Matter-Filled Spacetimes
  13. Connections Between Complex Geometry and General Relativity

Complex Geometry and Mathematical Physics:
Classical and Quantum Singularities of Space-Times (Book III-B)

DETAILS
EXPLANATIONS

This volume is Book III-B of the Complex Geometry and Mathematical Physics series. It focuses on the theory of space-time singularities in both classical general relativity and quantum gravity.

Major topics include:

The book is part of the larger research project Differential Geometry, Partial Differential Equations and Mathematical Physics, which explores modern connections between geometric analysis and gravitational physics.

TABLE OF CONTENTS

A complete official chapter-by-chapter table of contents has not yet been publicly released in the bibliographic sources currently available. However, the published synopsis indicates that the book covers the following principal themes:

  1. Classical Space-Time Singularities
  2. Curvature Singularities
  3. Bundle Boundary Constructions
  4. Quantum Probes of Singularities
  5. Horowitz–Marolf Theory
  6. Resolution of Negative-Mass Naked Singularities
  7. Loop Quantum Gravity and Singularity Resolution
  8. Mathematical Analysis of Black Holes
  9. Gravitational Collapse
  10. Stability of Black-Hole Exteriors
  11. Wave Functions of Black Holes
  12. Marginally Trapped Surfaces
  13. Geometry of the Second Fundamental Form
  14. Lorentzian Manifold Techniques
  15. Applications of Complex Geometry to Relativity and Quantum Gravity
  16. Diederich–Fornæss Worm Domains and Related Geometric Pathologies

Lebesgue's Theory of Singular Integrals:
Foundations of Modern Harmonic Analysis

DETAILS
EXPLANATIONS

This book presents an English translation of Henri Lebesgue's landmark 1909 paper Sur les Intégrales Singulières ("On Singular Integrals"), making a historically important French mathematical work accessible to modern readers. The volume combines the original theory with historical commentary and pedagogical material.

The author provides:

The book is intended for advanced undergraduate students, graduate students, researchers, and historians of mathematics interested in Fourier analysis, integration theory, and harmonic analysis.

TABLE OF CONTENTS

The available publisher information lists the following chapter structure:

  1. Historical Developments
  2. Convergence of Singular Integrals and Applications in Function Approximations
  3. Basic Identities
  4. Continuous Functions: Integral of Product Functions
  5. Convergence and Term-by-Term Integrability of Function Sequences
  6. Linear Functional Operations
  7. Classical Theorems on Singular Integrals
  8. Various Named Integrals
  9. Problems of Moments

Additional Features


T. Y. Lam

Excursions in Ring Theory

DETAILS
EXPLANATIONS

This self-contained graduate text provides a comprehensive treatment of major developments in ring theory over roughly the last eighty years. It serves as the third volume in a trilogy that includes the books A First Course in Noncommutative Rings and Lectures on Modules and Rings.

The book focuses on several important topics in modern noncommutative algebra, including:

The text contains extensive exercises and is intended for graduate students, researchers, and mathematicians seeking a deeper understanding of contemporary ring theory and module theory.

TABLE OF CONTENTS

The currently available publisher information lists the following chapters:

  1. Introduction to Regular Rings
  2. Fitting Theory and Modules Over Regular Rings
  3. Generalized Inverses and Rings with Involutions
  4. Exchange Rings and Suitable Rings
  5. Clean Rings and Their Variations
  6. Cancellation, Substitution, and Stable Range
ABOUT THE AUTHOR

T. Y. Lam is Professor Emeritus of Mathematics at the University of California, Berkeley. His research spans ring theory, field theory, group theory, and the history of mathematics. He is well known for a series of influential graduate texts in algebra and received the Leroy P. Steele Prize for mathematical exposition.

S. Mohammad Mozaffari

Planetary Astronomy in the Classical Islamic Period:
Wondering About the Wanderers

DETAILS
EXPLANATIONS

This scholarly work presents the first comprehensive study of planetary observations preserved in the Hakimi Zīj of the Egyptian astronomer Ibn Yunus. The book investigates how astronomers of the 9th–10th centuries observed planets, tested astronomical theories, and refined mathematical models inherited from the Ptolemaic tradition.

The author reconstructs observational practices employed by medieval Islamic astronomers, including:

The study analyzes observations and theories associated with several important astronomers, including:

A central argument of the book is that classical Islamic astronomy was not merely a preservation of Greek science but a vibrant tradition characterized by empirical testing, methodological innovation, and theoretical refinement.

TABLE OF CONTENTS

A complete official chapter-by-chapter table of contents was not available in the publicly accessible sources at the time of publication. However, the publisher's description indicates that the book covers the following major themes:

  1. Introduction to Classical Islamic Planetary Astronomy
  2. Planetary Observations in the Hakimi Zīj
  3. Observational Programs of Early Islamic Astronomers
  4. Methodological Relations Between Observation and Theory
  5. Conjunctions, Appulses, and Occultations
  6. Reconstruction of Historical Sky Configurations
  7. Precision, Visibility, and Astronomical Instruments
  8. Testing Ptolemaic Planetary Models
  9. Identification of Model Anomalies
  10. Corrective Strategies (Istidrāk and Taṣḥīḥ)
  11. Contributions of Habash, Al-Mahani, Ibn Yunus, and the Banū Amajur
  12. Comparative Analysis of Al-Battani, Ibn al-Aʿlam, Kushyar, and Al-Biruni
  13. From Medieval Ephemerides to Modern Sky-Simulation Software
  14. Empirical Methodology in Islamic Astronomy
  15. Historical Significance for the Development of Astronomy
  16. Conclusions and Future Research Directions
ABOUT THE AUTHOR

S. Mohammad Mozaffari is an Iranian historian of science specializing in medieval Islamic astronomy, observational practices, and the relationship between astronomical observations and mathematical theories. He has published extensively in the history of astronomy and serves on the editorial boards of several scholarly journals in the field.