ESI Lectures in Mathematics and Physics
ISBN 978-3-03719-051-7
June 2008, 549 pages, softcover, 17 x 24 cm.
This book provides an introduction to and survey of recent developments in pseudo-Riemannian geometry, including applications in mathematical physics, by leading experts in the field. Topics covered are:
Classification of pseudo-Riemannian symmetric spaces
Holonomy groups of Lorentzian and pseudo-Riemannian manifolds
Hypersymplectic manifolds
Anti-self-dual conformal structures in neutral signature and integrable systems
Neutral Kahler surfaces and geometric optics
Geometry and dynamics of the Einstein universe
Essential conformal structures and conformal transformations in pseudo-Riemannian geometry
The causal hierarchy of spacetimes
Geodesics in pseudo-Riemannian manifolds
Lorentzian symmetric spaces in supergravity
Generalized geometries in supergravity
Einstein metrics with Killing leaves
The book is addressed to advanced students as well as to researchers in differential geometry, global analysis, general relativity and string theory. It shows essential differences between the geometry on manifolds with positive definite metrics and on those with indefinite metrics, and highlights the interesting new geometric phenomena, which naturally arise in the indefinite metric case. The reader finds a description of the present state of art in the field as well as open problems, which can stimulate further research.
IRMA Lectures in Mathematics and Theoretical Physics Vol. 12
ISBN 978-3-03719-047-0
June 2008, 140 pages, softcover, 17 x 24 cm.
The volume starts with a lecture course by P. Etingof on tensor categories (notes by D. Calaque). This course is an introduction to tensor categories, leading to topics of recent research such as realizability of fusion rings, Ocneanu rigidity, module categories, weak Hopf algebras, Morita theory for tensor categories, lifting theory, categorical dimensions, Frobenius*Perron dimensions, and the classification of tensor categories.
The remainder of the book consists of three detailed expositions on associators and the Vassiliev invariants of knots, classical and quantum integrable systems and elliptic algebras, and the groups of algebra automorphisms of quantum groups. The preface sets the results presented in perspective.
Directed at research mathematicians and theoretical physicists as well as graduate students, the volume gives an overview of the ongoing research in the domain of quantum groups, an important subject of current mathematical physics.
ISBN: 978-3-527-40760-6
Hardcover
240 pages
October 2008
This introduction to Monte Carlo methods seeks to identify and study the unifying elements that underlie their effective application. Initial chapters provide a short treatment of the probability and statistics needed as background, enabling those without experience in Monte Carlo techniques to apply these ideas to their research.
It focuses on two basic themes: The first is the importance of random walks as they occur both in natural stochastic systems and in their relationship to integral and differential equations. The second theme is that of variance reduction in general and importance sampling in particular as a technique for efficient use of the methods. Random walks are introduced with an elementary example in which the modeling of radiation transport arises directly from a schematic probabilistic description of the interaction of radiation with matter. Building on this example, the relationship between random walks and integral equations is outlined. The applicability of these ideas to other problems is shown by a clear and elementary introduction to the solution of the Schrodinger equation by random walks.
The text includes sample problems that readers can solve by themselves to illustrate the content of each chapter.
This is the second, completely revised and extended edition of the successful monograph, which brings the treatment up to date and incorporates the many advances in Monte Carlo techniques and their applications, while retaining the original elementary but general approach.
1. What is Monte Carlo
2. A Bit of Probability Theory
3. Sampling Random Variables
4. Evaluation of Finite-Dimensional Integrals and Variance Reduction
5. Random Walks, Integral Equations and Variance Reduction
6. Simulations of Stochastic Systems: Radiation Transport
7. Statistical Physics
8. Quantum Monte Carlo
9. Pseudorandom Numbers
ISBN-13: 978-0-19-921944-5
Estimated publication date: December 2008
3900 pages, 246x189 mm
Description
Collection of works of one of the eminent mathematicians of the 20th Century.
Spanning fifty years of science
Introduction from Professor Sir Roger Penrose
Includes previously unpublished theses and Twistor Newsletter articles
Professor Sir Roger Penrose is one of the truly original thinkers of our time and has made several remarkable contributions to science from quantum physics and theories of human consciousness to relativity theory and observations on the structure of the universe in over 240 scientific publications. Here his works, spanning 50 years of science and including his previously unpublished theses, have been collected and arranged chronologically over six volumes, each with an introduction from the author.
Readership: Graduates and researchers in mathematics and physics
ISBN-13: 978-0-19-955951-0
Estimated publication date: January 2009
The book begins with a brief review of supersymmetry, and the construction of the minimal supersymmetric standard model and approaches to supersymmetry breaking. General non-perturbative methods are also reviewed leading to the development of holomorphy and the Affleck-Dine-Seiberg superpotential as powerful tools for analysing supersymmetric theories. Seiberg duality is discussed in detail, with many example applications provided, with special attention paid to its use in understanding dynamical supersysmmetry breaking. The Seiberg-Witten theory of monopoles is introduced through the analysis of simpler N=1 analogues. Superconformal field theories are described along with the most recent development known as "amaximization". Supergravity theories are examined in 4, 10, and 11 dimensions, allowing for a discussion of anomaly and gaugino mediation, and setting the stage for the anti- de Sitter/conformal field theory correspondence. This book is unique in containing an overview of the important developments in supersymmetry since the publication of "Suppersymmetry and Supergravity" by Wess and Bagger. It also strives to cover topics that are of interest to both formal and phenomenological theorists.
Readership: Graduate students and researchers in physics, cosmology, and mathematics.
1. Introduction to Supersymmetry
2. SUSY Lagrangians
3. SUSY Gauge Theories
4. The Minimal Supersymmetric Standard Model
5. SUSY Breaking and the MSSM
6. Gauge Mediation
7. Nonperturbative Results
8. Holomorphy
9. The Affleck-Dine-Seiberg Superpotential
10. Seiberg Duality for SUSY QCD
11. More Seiberg Duality
12. Dynamical SUSY breaking
13. The Seiberg-Witten Theory
14. Superconformal Field Theories
15. Supergravity
16. Anomaly and Guagino Mediation
17. Introduction to the Ads/CFT Correspondence
A. Spinors and Pauli Matrices
B. Group Theory
Paperback (ISBN-13: 9780521068871)
1 line figure 1 halftone
Page extent: 224 pages
Size: 229 x 152 (Standard)
Weight: 0.362 kg
Between 1814 and 1831, the great French mathematician A. L. Cauchy created practically single-handedly a new branch of pure mathematics. Complex function theory was and remains of central importance, and its creation marked the start of one of the most exciting periods in the development of mathematics. In this book Dr Smithies analyses the process whereby Cauchy created the basic structure of complex analysis, describing first the eighteenth-century background before proceeding to examine the stages of Cauchyfs own work, culminating in the proof of the residue theorem and his work on expansions in power series. Smithies describes how Cauchy overcame difficulties including false starts and contradictions brought about by over-ambitious assumptions, as well as the improvements that came about as the subject developed in Cauchyfs hands. Controversies associated with the birth of complex function theory are described in detail. Throughout, new light is thrown on Cauchyfs thinking during this watershed period. This book makes use of the whole spectrum of available original sources; it will be recognised as the authoritative work on the creation of complex function theory.
* New analyses will change the perception of the chronology of Cauchyfs achievements * Controversies associated with subjectfs birth are fully explored; contributions of others are also examined * First book to use whole spectrum of available original sources
1. Introduction; 2. The background to Cauchyfs work on complex function theory; 3. Cauchyfs 1814 memoir on definite integrals; 4. Miscellaneous contributions (1815*1825); 5. The 1825 memoir and associated papers; 6. The calculus of residues; 7. The Lagrange series and the Turin memoirs; 8. Summary and conclusions; References.