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Extensions of the Stability Theorem of the Minkowski Space in General Relativity
A famous result of Christodoulou and Klainerman is the global nonlinear stability of Minkowski spacetime. In this book, Bieri and Zipser provide two extensions to this result. In the first part, Bieri solves the Cauchy problem for the Einstein vacuum equations with more general, asymptotically flat initial data, and describes precisely the asymptotic behavior. In particular, she assumes less decay in the power of $r$ and one less derivative than in the Christodoulou-Klainerman result. She proves that in this case, too, the initial data, being globally close to the trivial data, yields a solution which is a complete spacetime, tending to the Minkowski spacetime at infinity along any geodesic....
Global Healing
Read an interview with Karen Thornber. In Global Healing: Literature, Advocacy, Care, Karen Laura Thornber analyzes how narratives from diverse communities globally engage with a broad variety of diseases and other serious health conditions and advocate for empathic, compassionate, and respectful care that facilitates healing and enables wellbeing. The three parts of this book discuss writings from Africa, the Americas, Asia, Europe, the Middle East, and Oceania that implore societies to shatter the devastating social stigmas which prevent billions from accessing effective care; to increase the availability of quality person-focused healthcare; and to prioritize partnerships that facilitate healing and enable wellbeing for both patients and loved ones. Thornber’s Global Healing remaps the contours of comparative literature, world literature, the medical humanities, and the health humanities. Watch a video interview with Thornber by the Mahindra Humanities Center, part of their conversations on Covid-19. Read an interview with Thornber on Brill's Humanities Matter blog.
The Inscription of Things
Why would an inkstone have a poem inscribed on it? Early modern Chinese writers did not limit themselves to working with brushes and ink, and their texts were not confined to woodblock-printed books or the boundaries of the paper page. Poets carved lines of verse onto cups, ladles, animal horns, seashells, walking sticks, boxes, fans, daggers, teapots, and musical instruments. Calligraphers left messages on the implements ordinarily used for writing on paper. These inscriptions—terse compositions in verse or epigrammatic prose—relate in complex ways to the objects on which they are written. Thomas Kelly develops a new account of the relationship between Chinese literature and material cu...
Heat Kernel and Analysis on Manifolds
The heat kernel has long been an essential tool in both classical and modern mathematics but has become especially important in geometric analysis as a result of major innovations beginning in the 1970s. The methods based on heat kernels have been used in areas as diverse as analysis, geometry, and probability, as well as in physics. This book is a comprehensive introduction to heat kernel techniques in the setting of Riemannian manifolds, which inevitably involves analysis of the Laplace-Beltrami operator and the associated heat equation. The first ten chapters cover the foundations of the subject, while later chapters deal with more advanced results involving the heat kernel in a variety o...
Geometric Relativity
Many problems in general relativity are essentially geometric in nature, in the sense that they can be understood in terms of Riemannian geometry and partial differential equations. This book is centered around the study of mass in general relativity using the techniques of geometric analysis. Specifically, it provides a comprehensive treatment of the positive mass theorem and closely related results, such as the Penrose inequality, drawing on a variety of tools used in this area of research, including minimal hypersurfaces, conformal geometry, inverse mean curvature flow, conformal flow, spinors and the Dirac operator, marginally outer trapped surfaces, and density theorems. This is the fir...
Fifth International Congress of Chinese Mathematicians
This two-part volume represents the proceedings of the Fifth International Congress of Chinese Mathematicians, held at Tsinghua University, Beijing, in December 2010. The Congress brought together eminent Chinese and overseas mathematicians to discuss the latest developments in pure and applied mathematics. Included are 60 papers based on lectures given at the conference.
Sacred Language, Vernacular Difference
How Arabic influenced the evolution of vernacular literatures and anticolonial thought in Egypt, Indonesia, and Senegal Sacred Language, Vernacular Difference offers a new understanding of Arabic’s global position as the basis for comparing cultural and literary histories in countries separated by vast distances. By tracing controversies over the use of Arabic in three countries with distinct colonial legacies, Egypt, Indonesia, and Senegal, the book presents a new approach to the study of postcolonial literatures, anticolonial nationalisms, and the global circulation of pluralist ideas. Annette Damayanti Lienau presents the largely untold story of how Arabic, often understood in Africa an...
Lagrangian Intersection Floer Theory
This is a two-volume series research monograph on the general Lagrangian Floer theory and on the accompanying homological algebra of filtered $A_\infty$-algebras. This book provides the most important step towards a rigorous foundation of the Fukaya category in general context. In Volume I, general deformation theory of the Floer cohomology is developed in both algebraic and geometric contexts. An essentially self-contained homotopy theory of filtered $A_\infty$ algebras and $A_\infty$ bimodules and applications of their obstruction-deformation theory to the Lagrangian Floer theory are presented. Volume II contains detailed studies of two of the main points of the foundation of the theory: transversality and orientation. The study of transversality is based on the virtual fundamental chain techniques (the theory of Kuranishi structures and their multisections) and chain level intersection theories. A detailed analysis comparing the orientations of the moduli spaces and their fiber products is carried out. A self-contained account of the general theory of Kuranishi structures is also included in the appendix of this volume.
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Chern-Simons Gauge Theory: 20 Years After
In 1989, Edward Witten discovered a deep relationship between quantum field theory and knot theory, and this beautiful discovery created a new field of research called Chern-Simons theory. This field has the remarkable feature of intertwining a large number of diverse branches of research in mathematics and physics, among them low-dimensional topology, differential geometry, quantum algebra, functional and stochastic analysis, quantum gravity, and string theory. The 20-year anniversary of Witten's discovery provided an opportunity to bring together researchers working in Chern-Simons theory for a meeting, and the resulting conference, which took place during the summer of 2009 at the Max Planck Institute for Mathematics in Bonn, included many of the leading experts in the field. This volume documents the activities of the conference and presents several original research articles, including another monumental paper by Witten that is sure to stimulate further activity in this and related fields. This collection will provide an excellent overview of the current research directions and recent progress in Chern-Simons gauge theory.
