Conformal Dimension - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Conformal Dimension write by John M. Mackay. This book was released on 2010. Conformal Dimension available in PDF, EPUB and Kindle. Conformal dimension measures the extent to which the Hausdorff dimension of a metric space can be lowered by quasisymmetric deformations. Introduced by Pansu in 1989, this concept has proved extremely fruitful in a diverse range of areas, including geometric function theory, conformal dynamics, and geometric group theory. This survey leads the reader from the definitions and basic theory through to active research applications in geometric function theory, Gromov hyperbolic geometry, and the dynamics of rational maps, amongst other areas. It reviews the theory of dimension in metric spaces and of deformations of metric spaces. It summarizes the basic tools for estimating conformal dimension and illustrates their application to concrete problems of independent interest. Numerous examples and proofs are provided. Working from basic definitions through to current research areas, this book can be used as a guide for graduate students interested in this field, or as a helpful survey for experts. Background needed for a potential reader of the book consists of a working knowledge of real and complex analysis on the level of first- and second-year graduate courses.
Assouad Dimension and Fractal Geometry
Assouad Dimension and Fractal Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Assouad Dimension and Fractal Geometry write by Jonathan M. Fraser. This book was released on 2020-10-29. Assouad Dimension and Fractal Geometry available in PDF, EPUB and Kindle. The first thorough treatment of the Assouad dimension in fractal geometry, with applications to many fields within pure mathematics.
Two-Dimensional Conformal Geometry and Vertex Operator Algebras
Two-Dimensional Conformal Geometry and Vertex Operator Algebras - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Two-Dimensional Conformal Geometry and Vertex Operator Algebras write by Yi-Zhi Huang. This book was released on 2012-12-06. Two-Dimensional Conformal Geometry and Vertex Operator Algebras available in PDF, EPUB and Kindle. The theory of vertex operator algebras and their representations has been showing its power in the solution of concrete mathematical problems and in the understanding of conceptual but subtle mathematical and physical struc- tures of conformal field theories. Much of the recent progress has deep connec- tions with complex analysis and conformal geometry. Future developments, especially constructions and studies of higher-genus theories, will need a solid geometric theory of vertex operator algebras. Back in 1986, Manin already observed in Man) that the quantum theory of (super )strings existed (in some sense) in two entirely different mathematical fields. Under canonical quantization this theory appeared to a mathematician as the representation theories of the Heisenberg, Vir as oro and affine Kac- Moody algebras and their superextensions. Quantization with the help of the Polyakov path integral led on the other hand to the analytic theory of algebraic (super ) curves and their moduli spaces, to invariants of the type of the analytic curvature, and so on.He pointed out further that establishing direct mathematical connections between these two forms of a single theory was a big and important problem. On the one hand, the theory of vertex operator algebras and their repre- sentations unifies (and considerably extends) the representation theories of the Heisenberg, Virasoro and Kac-Moody algebras and their superextensions.
Conformal Field Theory
Conformal Field Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Conformal Field Theory write by Philippe Francesco. This book was released on 2012-12-06. Conformal Field Theory available in PDF, EPUB and Kindle. Filling an important gap in the literature, this comprehensive text develops conformal field theory from first principles. The treatment is self-contained, pedagogical, and exhaustive, and includes a great deal of background material on quantum field theory, statistical mechanics, Lie algebras and affine Lie algebras. The many exercises, with a wide spectrum of difficulty and subjects, complement and in many cases extend the text. The text is thus not only an excellent tool for classroom teaching but also for individual study. Intended primarily for graduate students and researchers in theoretical high-energy physics, mathematical physics, condensed matter theory, statistical physics, the book will also be of interest in other areas of theoretical physics and mathematics. It will prepare the reader for original research in this very active field of theoretical and mathematical physics.
Conformal Field Theory
Conformal Field Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Conformal Field Theory write by Sergei V Ketov. This book was released on 1995-02-28. Conformal Field Theory available in PDF, EPUB and Kindle. Conformal field theory is an elegant and powerful theory in the field of high energy physics and statistics. In fact, it can be said to be one of the greatest achievements in the development of this field. Presented in two dimensions, this book is designed for students who already have a basic knowledge of quantum mechanics, field theory and general relativity. The main idea used throughout the book is that conformal symmetry causes both classical and quantum integrability. Instead of concentrating on the numerous applications of the theory, the author puts forward a discussion of the general methods of conformal field theory as a physical theory. Hence the book provides in a self-contained way the necessary knowledge and “conformal” intuition which underline the various applications of conformal field theory. It is aimed to assist students and professionals in the study of the theory from its first principles and in applying the methods in their own research. The first of its kind, this book promises to give a detailed and comprehensive insight into the workings of conformal field theory.
