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The Coxeter Legacy by Harold Scott Macdonald Coxeter,Chandler Davis,Erich W. Ellers Pdf
This collection of essays on the legacy of mathematican Donald Coxeter is a mixture of surveys, updates, history, storytelling and personal memories covering both applied and abstract maths. Subjects include: polytopes, Coxeter groups, equivelar polyhedra, Ceva's theorum, and Coxeter and the artists.
Groups of Exceptional Type, Coxeter Groups and Related Geometries by N.S. Narasimha Sastry Pdf
The book deals with fundamental structural aspects of algebraic and simple groups, Coxeter groups and the related geometries and buildings. All contributing authors are very active researchers in the topics related to the theme of the book. Some of the articles provide the latest developments in the subject; some provide an overview of the current status of some important problems in this area; some survey an area highlighting the current developments; and some provide an exposition of an area to collect problems and conjectures. It is hoped that these articles would be helpful to a beginner to start independent research on any of these topics, as well as to an expert to know some of the latest developments or to consider some problems for investigation.
The Mathematical Legacy of Harish-Chandra by Harish-Chandra,Robert S. Doran,V. S. Varadarajan Pdf
Harish-Chandra was a mathematician of great power, vision, and remarkable ingenuity. His profound contributions to the representation theory of Lie groups, harmonic analysis, and related areas left researchers a rich legacy that continues today. This book presents the proceedings of an AMS Special Session entitled, ""Representation Theory and Noncommutative Harmonic Analysis: A Special Session Honoring the Memory of Harish-Chandra"", which marked 75 years since his birth and 15 years since his untimely death at age 60. Contributions to the volume were written by an outstanding group of internationally known mathematicians. Included are expository and historical surveys and original research papers.The book also includes talks given at the IAS Memorial Service in 1983 by colleagues who knew Harish-Chandra well. Also reprinted are two articles entitled, ""Some Recollections of Harish-Chandra"", by A. Borel, and ""Harish-Chandra's c-Function: A Mathematical Jewel"", by S. Helgason. In addition, an expository paper, ""An Elementary Introduction to Harish-Chandra's Work"", gives an overview of some of his most basic mathematical ideas with references for further study. This volume offers a comprehensive retrospective of Harish-Chandra's professional life and work. Personal recollections give the book particular significance. Readers should have an advanced-level background in the representation theory of Lie groups and harmonic analysis. For other wonderful titles written by this author see: ""Euler through Time: A New Look at Old Themes"", ""Supersymmetry for Mathematicians: An Introduction"", ""The Selected Works of V.S. Varadarajan"", and ""Algebra in Ancient and Modern Times"".
very small domain (environment) affects through analytic continuation the whole of Riemann surface, or analytic manifold . Riemann was a master at applying this principle and also the first who noticed and emphasized that a meromorphic function is determined by its 'singularities'. Therefore he is rightly regarded as the father of the huge 'theory of singularities' which is developing so quickly and whose importance (also for physics) can hardly be overe~timated. Amazing and mysterious for our cognition is the role of Euclidean space. Even today many philosophers believe (following Kant) that 'real space' is Euclidean and other spaces being 'abstract constructs of mathematicians, should not be called spaces'. The thesis is no longer tenable - the whole of physics testifies to that. Nevertheless, there is a grain of truth in the 3 'prejudice': E (three-dimensional Euclidean space) is special in a particular way pleasantly familiar to us - in it we (also we mathematicians!) feel particularly 'confident' and move with a sense of greater 'safety' than in non-Euclidean spaces. For this reason perhaps, Riemann space M stands out among the multitude of 'interesting geometries'. For it is: 1. Locally Euclidean, i. e. , M is a differentiable manifold whose tangent spaces TxM are equipped with Euclidean metric Uxi 2. Every submanifold M of Euclidean space E is equipped with Riemann natural metric (inherited from the metric of E) and it is well known how often such submanifolds are used in mechanics (e. g. , the spherical pendulum).
The Mathematical Legacy of Richard P. Stanley by Patricia Hersh,Thomas Lam,Pavlo Pylyavskyy,Victor Reiner Pdf
Richard Stanley's work in combinatorics revolutionized and reshaped the subject. His lectures, papers, and books inspired a generation of researchers. In this volume, these researchers explain how Stanley's vision and insights influenced and guided their own perspectives on the subject. As a valuable bonus, this book contains a collection of Stanley's short comments on each of his papers. This book may serve as an introduction to several different threads of ongoing research in combinatorics as well as giving historical perspective.
The Legacy of the Inverse Scattering Transform in Applied Mathematics by J. L. Bona,Roy Choudhury,David Kaup,Ams-IMS-Siam Joint Summer Research Conference on the Legacy of Inverse Scattering Transfor Pdf
Swift progress and new applications characterize the area of solitons and the inverse scattering transform. There are rapid developments in current nonlinear optical technology: Larger intensities are more available; pulse widths are smaller; relaxation times and damping rates are less significant. In keeping with these advancements, exactly integrable soliton equations, such as $3$-wave resonant interactions and second harmonic generation, are becoming more and more relevant in experimental applications. Techniques are now being developed for using these interactions to frequency convert high intensity sources into frequency regimes where there are no lasers. Other experiments involve using these interactions to develop intense variable frequency sources, opening up even more possibilities. This volume contains new developments and state-of-the-art research arising from the conference on the ""Legacy of the Inverse Scattering Transform"" held at Mount Holyoke College (South Hadley, MA). Unique to this volume is the opening section, ""Reviews"". This part of the book provides reviews of major research results in the inverse scattering transform (IST), on the application of IST to classical problems in differential geometry, on algebraic and analytic aspects of soliton-type equations, on a new method for studying boundary value problems for integrable partial differential equations (PDEs) in two dimensions, on chaos in PDEs, on advances in multi-soliton complexes, and on a unified approach to integrable systems via Painleve analysis. This conference provided a forum for general exposition and discussion of recent developments in nonlinear waves and related areas with potential applications to other fields. The book will be of interest to graduate students and researchers interested in mathematics, physics, and engineering.
Notes on Coxeter Transformations and the McKay Correspondence by Rafael Stekolshchik Pdf
Here is a key text on the subject of representation theory in finite groups. The pages of this excellent little book, prepared by Rafael Stekolshchik, contain a number of new proofs relating to Coxeter Transformations and the McKay Correspondence. They include ideas and formulae from a number of luminaries including J. N. Bernstein, I. M. Gelfand and V. A. Ponomarev, as well as material from Coxeter and McKay themselves. Many other authors have material published here too.
M.C. Escher’s Legacy by Michele Emmer,Doris Schattschneider Pdf
Softcover printing of a popular title (h/c sold over 400 copies in North America) at a price that will make it accessible to a much wider audience Richly illustrated with original art works in addition to well-known and little-known works by Escher A CD-ROM complements the articles, containing color illustrations of work by contemporary artists, movies, animations, and other demonstrations
"The CD-ROM is an extension of the book. It contains color versions of many of the art works that are shown in the book in black and white, as well as additional work by the artists. It gives vignettes of the conference ... animations, short videos, and interactive puzzles."--Page vii.
Coxeter Groups and Hopf Algebras by Marcelo Aguiar,Swapneel Mahajan,Swapneel Arvind Mahajan Pdf
An important idea in the work of G.-C. Rota is that certain combinatorial objects give rise to Hopf algebras that reflect the manner in which these objects compose and decompose. Recent work has seen the emergence of several interesting Hopf algebras of this kind, which connect diverse subjects such as combinatorics, algebra, geometry, and theoretical physics. This monograph presents a novel geometric approach using Coxeter complexes and the projection maps of Tits for constructingand studying many of these objects as well as new ones. The first three chapters introduce the necessary background ideas making this work accessible to advanced graduate students. The later chapters culminate in a unified and conceptual construction of several Hopf algebras based on combinatorialobjects which emerge naturally from the geometric viewpoint. This work lays a foundation and provides new insights for further development of the subject. To read more about Coxeter groups see The Coxeter Legacy: Reflections and Projections. Information for our distributors: Titles in this series are copublished with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Aspects Of Infinite Groups: A Festschrift In Honor Of Anthony Gaglione by Benjamin Fine,Gerhard Rosenberger,Dennis Spellman Pdf
This book is a festschrift in honor of Professor Anthony Gaglione's sixtieth birthday. This volume presents an excellent mix of research and expository articles on various aspects of infinite group theory. The papers give a broad overview of present research in infinite group theory in general, and combinatorial group theory and non-Abelian group-based cryptography in particular. They also pinpoint the interactions between combinatorial group theory and mathematical logic, especially model theory.
Groups and Symmetries by Yvette Kosmann-Schwarzbach Pdf
- Combines material from many areas of mathematics, including algebra, geometry, and analysis, so students see connections between these areas - Applies material to physics so students appreciate the applications of abstract mathematics - Assumes only linear algebra and calculus, making an advanced subject accessible to undergraduates - Includes 142 exercises, many with hints or complete solutions, so text may be used in the classroom or for self study
The Best Writing on Mathematics 2011 by Mircea Pitici Pdf
The year's finest writing on mathematics from around the world This anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2011 makes available to a wide audience many articles not easily found anywhere else—and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Ian Hacking discusses the salient features that distinguish mathematics from other disciplines of the mind; Doris Schattschneider identifies some of the mathematical inspirations of M. C. Escher's art; Jordan Ellenberg describes compressed sensing, a mathematical field that is reshaping the way people use large sets of data; Erica Klarreich reports on the use of algorithms in the job market for doctors; and much, much more. In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed physicist and mathematician Freeman Dyson. This book belongs on the shelf of anyone interested in where math has taken us—and where it is headed.
For more than five decades Bertram Kostant has been one of the major architects of modern Lie theory. Virtually all his papers are pioneering with deep consequences, many giving rise to whole new fields of activities. His interests span a tremendous range of Lie theory, from differential geometry to representation theory, abstract algebra, and mathematical physics. It is striking to note that Lie theory (and symmetry in general) now occupies an ever increasing larger role in mathematics than it did in the fifties. Now in the sixth decade of his career, he continues to produce results of astonishing beauty and significance for which he is invited to lecture all over the world. This is the first volume (1955-1966) of a five-volume set of Bertram Kostant's collected papers. A distinguished feature of this first volume is Kostant's commentaries and summaries of his papers in his own words.
Geometric Methods in Physics by Piotr Kielanowski,S. Twareque Ali,Alexander Odesskii,Anatol Odzijewicz,Martin Schlichenmaier,Theodore Voronov Pdf
The Białowieża workshops on Geometric Methods in Physics, taking place in the unique environment of the Białowieża natural forest in Poland, are among the important meetings in the field. Every year some 80 to 100 participants both from mathematics and physics join to discuss new developments and to interchange ideas. The current volume was produced on the occasion of the XXXI meeting in 2012. For the first time the workshop was followed by a School on Geometry and Physics, which consisted of advanced lectures for graduate students and young researchers. Selected speakers of the workshop were asked to contribute, and additional review articles were added. The selection shows that despite its now long tradition the workshop remains always at the cutting edge of ongoing research. The XXXI workshop had as a special topic the works of the late Boris Vasilievich Fedosov (1938–2011) who is best known for a simple and very natural construction of a deformation quantization for any symplectic manifold, and for his contributions to index theory.
