MOONSHINE BEYOND THE MONSTER THE BRIDGE CONNECTING ALGEBRA MODULAR FORMS AND PHYSICS CAMBRIDGE MONOGRAPHS ON MATHEMATICAL PHYSICS

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Author : Terry Gannon
ISBN : 1139457802
Genre : Science
File Size : 77.35 MB
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This book was originally published in 2006. Moonshine forms a way of explaining the mysterious connection between the monster finite group and modular functions from classical number theory. The theory has evolved to describe the relationship between finite groups, modular forms and vertex operator algebras. Moonshine Beyond the Monster describes the general theory of Moonshine and its underlying concepts, emphasising the interconnections between mathematics and mathematical physics. Written in a clear and pedagogical style, this book is ideal for graduate students and researchers working in areas such as conformal field theory, string theory, algebra, number theory, geometry and functional analysis. Containing over a hundred exercises, it is also a suitable textbook for graduate courses on Moonshine and as supplementary reading for courses on conformal field theory and string theory.

Author : Terry Gannon
ISBN : 0521141885
Genre : Science
File Size : 52.91 MB
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Moonshine forms a way of explaining the mysterious connection between the monster finite group and modular functions from classical number theory. The theory has evolved to describe the relationship between finite groups, modular forms and vertex operator algebras. Moonshine Beyond the Monster, the first book of its kind, describes the general theory of Moonshine and its underlying concepts, emphasising the interconnections between modern mathematics and mathematical physics. Written in a clear and pedagogical style, this book is ideal for graduate students and researchers working in areas such as conformal field theory, string theory, algebra, number theory, geometry, and functional analysis. Containing over a hundred exercises, it is also a suitable textbook for graduate courses on Moonshine and as supplementary reading for courses on conformal field theory and string theory.

Author : Terry Gannon
ISBN : 0521835313
Genre : Science
File Size : 72.84 MB
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Moonshine forms a way of explaining the mysterious connection between the monster finite group and modular functions from classical number theory. The theory has evolved to describe the relationship between finite groups, modular forms and vertex operator algebras. Moonshine Beyond the Monster, the first book of its kind, describes the general theory of Moonshine and its underlying concepts, emphasising the interconnections between modern mathematics and mathematical physics. Written in a clear and pedagogical style, this book is ideal for graduate students and researchers working in areas such as conformal field theory, string theory, algebra, number theory, geometry, and functional analysis. Containing over a hundred exercises, it is also a suitable textbook for graduate courses on Moonshine and as supplementary reading for courses on conformal field theory and string theory.

Author : Mark Ronan
ISBN : 9780192807236
Genre : History
File Size : 49.30 MB
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Imagine a giant snowflake in 196,884 dimensions... This is the story of a mathematical quest that began two hundred years ago in revolutionary France, which led to the biggest collaboration ever between mathematicians across the world, and revealed the 'Monster' - a structure of beauty and complexity. And it is a story that is not yet over, for we have yet to understand the deep significance of the Monster - and its tantalising hints of connections with the physical structure of spacetime. Once we understand the full nature of the Monster, we may well have revealed a whole new and deeper understanding of the nature of our Universe.

Author : Manjul Bhargava
ISBN : 9781470436780
Genre : Atlas of finite groups
File Size : 72.14 MB
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Classification of Finite Simple Groups, one of the most monumental accomplishments of modern mathematics, was announced in 1983 with the proof completed in 2004. Since then, it has opened up a new and powerful strategy to approach and resolve many previously inaccessible problems in group theory, number theory, combinatorics, coding theory, algebraic geometry, and other areas of mathematics. This strategy crucially utilizes various information about finite simple groups, part of which is catalogued in the Atlas of Finite Groups (John H. Conway et al.), and in An Atlas of Brauer Characters (Christoph Jansen et al.). It is impossible to overestimate the roles of the Atlases and the related computer algebra systems in the everyday life of researchers in many areas of contemporary mathematics. The main objective of the conference was to discuss numerous applications of the Atlases and to explore recent developments and future directions of research, with focus on the interaction between computation and theory and applications to number theory and algebraic geometry. The papers in this volume are based on talks given at the conference. They present a comprehensive survey on current research in all of these fields.

Author : Erick J. Weinberg
ISBN : 9781139576376
Genre : Science
File Size : 76.82 MB
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Classical solutions play an important role in quantum field theory, high-energy physics and cosmology. Real-time soliton solutions give rise to particles, such as magnetic monopoles, and extended structures, such as domain walls and cosmic strings, that have implications for early universe cosmology. Imaginary-time Euclidean instantons are responsible for important nonperturbative effects, while Euclidean bounce solutions govern transitions between metastable states. Written for advanced graduate students and researchers in elementary particle physics, cosmology and related fields, this book brings the reader up to the level of current research in the field. The first half of the book discusses the most important classes of solitons: kinks, vortices and magnetic monopoles. The cosmological and observational constraints on these are covered, as are more formal aspects, including BPS solitons and their connection with supersymmetry. The second half is devoted to Euclidean solutions, with particular emphasis on Yang–Mills instantons and on bounce solutions.

Self-contained and comprehensive, this definitive new edition of Gravity and Strings is a unique resource for graduate students and researchers in theoretical physics. From basic differential geometry through to the construction and study of black-hole and black-brane solutions in quantum gravity - via all the intermediate stages - this book provides a complete overview of the intersection of gravity, supergravity, and superstrings. Now fully revised, this second edition covers an extensive array of topics, including new material on non-linear electric-magnetic duality, the electric-tensor formalism, matter-coupled supergravity, supersymmetric solutions, the geometries of scalar manifolds appearing in 4- and 5-dimensional supergravities, and much more. Covering reviews of important solutions and numerous solution-generating techniques, and accompanied by an exhaustive index and bibliography, this is an exceptional reference work.

Author : Robert Friedman
ISBN : 9780821805916
Genre : Science
File Size : 65.18 MB
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The lectures in this volume provide a perspective on how 4-manifold theory was studied before the discovery of modern-day Seiberg-Witten theory. One reason the progress using the Seiberg-Witten invariants was so spectacular was that those studying $SU(2)$-gauge theory had more than ten years' experience with the subject. The tools had been honed, the correct questions formulated, and the basic strategies well understood. The knowledge immediately bore fruit in the technically simpler environment of the Seiberg-Witten theory. Gauge theory long predates Donaldson's applications of the subject to 4-manifold topology, where the central concern was the geometry of the moduli space. One reason for the interest in this study is the connection between the gauge theory moduli spaces of a Kahler manifold and the algebro-geometric moduli space of stable holomorphic bundles over the manifold. The extra geometric richness of the $SU(2)$-moduli spaces may one day be important for purposes beyond the algebraic invariants that have been studied to date. It is for this reason that the results presented in this volume will be essential.

Author : Lev V. Prokhorov
ISBN : 9781139500906
Genre : Science
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The principles of gauge symmetry and quantization are fundamental to modern understanding of the laws of electromagnetism, weak and strong subatomic forces and the theory of general relativity. Ideal for graduate students and researchers in theoretical and mathematical physics, this unique book provides a systematic introduction to Hamiltonian mechanics of systems with gauge symmetry. The book reveals how gauge symmetry may lead to a non-trivial geometry of the physical phase space and studies its effect on quantum dynamics by path integral methods. It also covers aspects of Hamiltonian path integral formalism in detail, along with a number of related topics such as the theory of canonical transformations on phase space supermanifolds, non-commutativity of canonical quantization and elimination of non-physical variables. The discussion is accompanied by numerous detailed examples of dynamical models with gauge symmetries, clearly illustrating the key concepts.

Author : Béla Bollobás
ISBN : 9781139936668
Genre : Mathematics
File Size : 40.6 MB
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Can a Christian escape from a lion? How quickly can a rumour spread? Can you fool an airline into accepting oversize baggage? Recreational mathematics is full of frivolous questions where the mathematician's art can be brought to bear. But play often has a purpose. In mathematics, it can sharpen skills, provide amusement, or simply surprise, and books of problems have been the stock-in-trade of mathematicians for centuries. This collection is designed to be sipped from, rather than consumed in one sitting. The questions range in difficulty: the most challenging offer a glimpse of deep results that engage mathematicians today; even the easiest prompt readers to think about mathematics. All come with solutions, many with hints, and most with illustrations. Whether you are an expert, or a beginner or an amateur mathematician, this book will delight for a lifetime.