Topology C Algebras And String Duality
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Topology C Algebras And String Duality
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Author : Jonathan R_osenberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-10-27
Topology C Algebras And String Duality written by Jonathan R_osenberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-27 with Mathematics categories.
String theory is the leading candidate for a physical theory that combines all the fundamental forces of nature, as well as the principles of relativity and quantum mechanics, into a mathematically elegant whole. The mathematical tools used by string theorists are highly sophisticated, and cover many areas of mathematics. As with the birth of quantum theory in the early 20th century, the mathematics has benefited at least as much as the physics from the collaboration. In this book, based on CBMS lectures given at Texas Christian University, Rosenberg describes some of the most recent interplay between string dualities and topology and operator algebras. The book is an interdisciplinary approach to duality symmetries in string theory. It can be read by either mathematicians or theoretical physicists, and involves a more-or-less equal mixture of algebraic topology, operator algebras, and physics. There is also a bit of algebraic geometry, especially in the last chapter. The reader is assumed to be somewhat familiar with at least one of these four subjects, but not necessarily with all or even most of them. The main objective of the book is to show how several seemingly disparate subjects are closely linked with one another, and to give readers an overview of some areas of current research, even if this means that not everything is covered systematically.
Topology C Algebras And String Duality
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Author : Jonathan Micah Rosenberg
language : en
Publisher:
Release Date : 2009
Topology C Algebras And String Duality written by Jonathan Micah Rosenberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Algebraic topology categories.
String theory is the leading candidate for a physical theory that combines all the fundamental forces of nature, as well as the principles of relativity and quantum mechanics, into a mathematically elegant whole. The mathematical tools used by string theorists are highly sophisticated, and cover many areas of mathematics. As with the birth of quantum theory in the early 20th century, the mathematics has benefited at least as much as the physics from the collaboration. In this book, based on CBMS lectures given at Texas Christian University, Rosenberg describes some of the most recent interplay.
Superstrings Geometry Topology And C Algebras
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Author : Robert S. Doran
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-10-13
Superstrings Geometry Topology And C Algebras written by Robert S. Doran and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-13 with Mathematics categories.
This volume contains the proceedings of an NSF-CBMS Conference held at Texas Christian University in Fort Worth, Texas, May 18-22, 2009. The papers, written especially for this volume by well-known mathematicians and mathematical physicists, are an outgrowth of the talks presented at the conference. Topics examined are highly interdisciplinary and include, among many other things, recent results on D-brane charges in $K$-homology and twisted $K$-homology, Yang-Mills gauge theory and connections with non-commutative geometry, Landau-Ginzburg models, $C^*$-algebraic non-commutative geometry and ties to quantum physics and topology, the rational homotopy type of the group of unitary elements in an Azumaya algebra, and functoriality properties in the theory of $C^*$-crossed products and fixed point algebras for proper actions. An introduction, written by Jonathan Rosenberg, provides an instructive overview describing common themes and how the various papers in the volume are interrelated and fit together. The rich diversity of papers appearing in the volume demonstrates the current interplay between superstring theory, geometry/topology, and non-commutative geometry. The book will be of interest to graduate students, mathematicians, mathematical physicists, and researchers working in these areas.
Tropical Geometry And Mirror Symmetry
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Author : Mark Gross
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-01-20
Tropical Geometry And Mirror Symmetry written by Mark Gross and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-20 with Mathematics categories.
Tropical geometry provides an explanation for the remarkable power of mirror symmetry to connect complex and symplectic geometry. The main theme of this book is the interplay between tropical geometry and mirror symmetry, culminating in a description of the recent work of Gross and Siebert using log geometry to understand how the tropical world relates the A- and B-models in mirror symmetry. The text starts with a detailed introduction to the notions of tropical curves and manifolds, and then gives a thorough description of both sides of mirror symmetry for projective space, bringing together material which so far can only be found scattered throughout the literature. Next follows an introduction to the log geometry of Fontaine-Illusie and Kato, as needed for Nishinou and Siebert's proof of Mikhalkin's tropical curve counting formulas. This latter proof is given in the fourth chapter. The fifth chapter considers the mirror, B-model side, giving recent results of the author showing how tropical geometry can be used to evaluate the oscillatory integrals appearing. The final chapter surveys reconstruction results of the author and Siebert for ``integral tropical manifolds.'' A complete version of the argument is given in two dimensions.
The Mutually Beneficial Relationship Of Graphs And Matrices
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Author : Richard A. Brualdi
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-07-06
The Mutually Beneficial Relationship Of Graphs And Matrices written by Richard A. Brualdi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-06 with Mathematics categories.
Graphs and matrices enjoy a fascinating and mutually beneficial relationship. This interplay has benefited both graph theory and linear algebra. In one direction, knowledge about one of the graphs that can be associated with a matrix can be used to illuminate matrix properties and to get better information about the matrix. Examples include the use of digraphs to obtain strong results on diagonal dominance and eigenvalue inclusion regions and the use of the Rado-Hall theorem to deduce properties of special classes of matrices. Going the other way, linear algebraic properties of one of the matrices associated with a graph can be used to obtain useful combinatorial information about the graph. The adjacency matrix and the Laplacian matrix are two well-known matrices associated to a graph, and their eigenvalues encode important information about the graph. Another important linear algebraic invariant associated with a graph is the Colin de Verdiere number, which, for instance, characterizes certain topological properties of the graph. This book is not a comprehensive study of graphs and matrices. The particular content of the lectures was chosen for its accessibility, beauty, and current relevance, and for the possibility of enticing the audience to want to learn more.
Families Of Riemann Surfaces And Weil Petersson Geometry
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Author : Scott A. Wolpert
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Families Of Riemann Surfaces And Weil Petersson Geometry written by Scott A. Wolpert and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
Provides a generally self-contained course for graduate students and postgraduates on deformations of hyperbolic surfaces and the geometry of the Weil-Petersson metric. It also offers an update for researchers; material not otherwise found in a single reference is included; and aunified approach is provided for an array of results.
Rudiments Of Ramsey Theory
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Author : Ron Graham
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-10-01
Rudiments Of Ramsey Theory written by Ron Graham and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-01 with Mathematics categories.
In every sufficiently large structure which has been partitioned there will always be some well-behaved structure in one of the parts. This takes many forms. For example, colorings of the integers by finitely many colors must have long monochromatic arithmetic progressions (van der Waerden's theorem); and colorings of the edges of large graphs must have monochromatic subgraphs of a specified type (Ramsey's theorem). This book explores many of the basic results and variations of this theory. Since the first edition of this book there have been many advances in this field. In the second edition the authors update the exposition to reflect the current state of the art. They also include many pointers to modern results. A co-publication of the AMS and CBMS.
Asymptotics Of Random Matrices And Related Models The Uses Of Dyson Schwinger Equations
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Author : Alice Guionnet
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-04-29
Asymptotics Of Random Matrices And Related Models The Uses Of Dyson Schwinger Equations written by Alice Guionnet and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-29 with Mathematics categories.
Probability theory is based on the notion of independence. The celebrated law of large numbers and the central limit theorem describe the asymptotics of the sum of independent variables. However, there are many models of strongly correlated random variables: for instance, the eigenvalues of random matrices or the tiles in random tilings. Classical tools of probability theory are useless to study such models. These lecture notes describe a general strategy to study the fluctuations of strongly interacting random variables. This strategy is based on the asymptotic analysis of Dyson-Schwinger (or loop) equations: the author will show how these equations are derived, how to obtain the concentration of measure estimates required to study these equations asymptotically, and how to deduce from this analysis the global fluctuations of the model. The author will apply this strategy in different settings: eigenvalues of random matrices, matrix models with one or several cuts, random tilings, and several matrices models.
Harmonic Analysis
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Author : Palle E.T. Jorgensen
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-10-30
Harmonic Analysis written by Palle E.T. Jorgensen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-30 with Mathematics categories.
There is a recent and increasing interest in harmonic analysis of non-smooth geometries. Real-world examples where these types of geometry appear include large computer networks, relationships in datasets, and fractal structures such as those found in crystalline substances, light scattering, and other natural phenomena where dynamical systems are present. Notions of harmonic analysis focus on transforms and expansions and involve dual variables. In this book on smooth and non-smooth harmonic analysis, the notion of dual variables will be adapted to fractals. In addition to harmonic analysis via Fourier duality, the author also covers multiresolution wavelet approaches as well as a third tool, namely, L2 spaces derived from appropriate Gaussian processes. The book is based on a series of ten lectures delivered in June 2018 at a CBMS conference held at Iowa State University.
From Riches To Raags 3 Manifolds Right Angled Artin Groups And Cubical Geometry
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Author : Daniel T. Wise
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
From Riches To Raags 3 Manifolds Right Angled Artin Groups And Cubical Geometry written by Daniel T. Wise and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
Wise describes a stream of geometric group theory connecting many of the classically considered groups arising in combinatorial group theory with right-angled Artin groups. He writes for new or seasoned researchers who have completed at least an introductory course of geometric groups theory or even just hyperbolic groups, but says some comfort with graphs of groups would be helpful. His topics include non-positively curved cube complexes, virtual specialness of malnormal amalgams, finiteness properties of the dual cube complex, walls in cubical small-cancellation theory, and hyperbolicity and quasiconvexity detection. Color drawings illustrate. Annotation ©2013 Book News, Inc., Portland, OR (booknews.com).