This book presents a novel development of fundamental and fascinating aspects of algebraic topology and mathematical physics: 'extra-ordinary' and further generalized cohomology theories enhanced to 'twisted' and differential-geometric form, with focus on, firstly, their rational approximation by generalized Chern character maps, and then, the resulting charge quantization laws in higher n-form gauge field theories appearing in string theory and the classification of topological quantum materials.Although crucial for understanding famously elusive effects in strongly interacting physics, the relevant higher non-abelian cohomology theory ('higher gerbes') has had an esoteric reputation and remains underdeveloped.Devoted to this end, this book's theme is that various generalized cohomology theories are best viewed through their classifying spaces (or moduli stacks) — not necessarily infinite-loop spaces — from which perspective the character map is really an incarnation of the fundamental theorem of rational homotopy theory, thereby not only uniformly subsuming the classical Chern character and a multitude of scattered variants that have been proposed, but now seamlessly applicable in the hitherto elusive generality of (twisted, differential, and) non-abelian cohomology.In laying out this result with plenty of examples, this book provides a modernized introduction and review of fundamental classical topics: 1. abstract homotopy theory via model categories; 2. generalized cohomology in its homotopical incarnation; 3. rational homotopy theory seen via homotopy Lie theory, whose fundamental theorem we recast as a (twisted) non-abelian de Rham theorem, which naturally induces the (twisted) non-abelian character map.
Conceptual progress in fundamental theoretical physics is linked with the search for the suitable mathematical structures that model the physical systems. Quantum field theory (QFT) has proven to be a rich source of ideas for mathematics for a long time. However, fundamental questions such as ``What is a QFT?'' did not have satisfactory mathematical answers, especially on spaces with arbitrary topology, fundamental for the formulation of perturbative string theory. This book contains a collection of papers highlighting the mathematical foundations of QFT and its relevance to perturbative string theory as well as the deep techniques that have been emerging in the last few years. The papers are organized under three main chapters: Foundations for Quantum Field Theory, Quantization of Field Theories, and Two-Dimensional Quantum Field Theories. An introduction, written by the editors, provides an overview of the main underlying themes that bind together the papers in the volume.
This book presents a novel development of fundamental and fascinating aspects of algebraic topology and mathematical physics: 'extra-ordinary' and further generalized cohomology theories enhanced to 'twisted' and differential-geometric form, with focus on, firstly, their rational approximation by generalized Chern character maps, and then, the resulting charge quantization laws in higher n-form gauge field theories appearing in string theory and the classification of topological quantum materials.Although crucial for understanding famously elusive effects in strongly interacting physics, the relevant higher non-abelian cohomology theory ('higher gerbes') has had an esoteric reputation and remains underdeveloped.Devoted to this end, this book's theme is that various generalized cohomology theories are best viewed through their classifying spaces (or moduli stacks) — not necessarily infinite-loop spaces — from which perspective the character map is really an incarnation of the fundamental theorem of rational homotopy theory, thereby not only uniformly subsuming the classical Chern character and a multitude of scattered variants that have been proposed, but now seamlessly applicable in the hitherto elusive generality of (twisted, differential, and) non-abelian cohomology.In laying out this result with plenty of examples, this book provides a modernized introduction and review of fundamental classical topics: 1. abstract homotopy theory via model categories; 2. generalized cohomology in its homotopical incarnation; 3. rational homotopy theory seen via homotopy Lie theory, whose fundamental theorem we recast as a (twisted) non-abelian de Rham theorem, which naturally induces the (twisted) non-abelian character map.
From the Pulitzer Prize–winning author of The Return comes a profoundly moving contemplation of the relationship between art and life. NAMED ONE OF THE BEST BOOKS OF THE YEAR BY THE WASHINGTON POST AND EVENING STANDARD After finishing his powerful memoir The Return, Hisham Matar, seeking solace and pleasure, traveled to Siena, Italy. Always finding comfort and clarity in great art, Matar immersed himself in eight significant works from the Sienese School of painting, which flourished from the thirteenth to the fifteenth centuries. Artists he had admired throughout his life, including Duccio and Ambrogio Lorenzetti, evoke earlier engagements he’d had with works by Caravaggio and Poussin, and the personal experiences that surrounded those moments. Including beautiful full-color reproductions of the artworks, A Month in Siena is about what occurred between Matar, those paintings, and the city. That month would be an extraordinary period in the writer’s life: an exploration of how art can console and disturb in equal measure, as well as an intimate encounter with a city and its inhabitants. This is a gorgeous meditation on how centuries-old art can illuminate our own inner landscape—current relationships, long-lasting love, grief, intimacy, and solitude—and shed further light on the present world around us. Praise for A Month in Siena “As exquisitely structured as The Return, driven by desire, yearning, loss, illuminated by the kindness of strangers. A Month in Siena is a triumph.”—Peter Carey
This book is concerned with defining the nature of the crisis of the Arab world, with tracing its possible development, and with charting the conditions of its possible outcomes, addressing the next decade from the vantage of 1986 rather than that of 1985.
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