INTRODUCTION TO LATTICE GEOMETRY THROUGH GROUP ACTION PDF Download
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Author: Boris Zhilinskii
Publisher: EDP Sciences
ISBN: 2759819523
Category : Science
Languages : fr
Pages : 271
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Book Description
An introduction to Louis Michel 's work.
Author: Boris Zhilinskii
Publisher: EDP Sciences
ISBN: 2759819523
Category : Science
Languages : fr
Pages : 271
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Book Description
An introduction to Louis Michel 's work.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 131
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Book Description
Author: B. Rosenfeld
Publisher: Springer Science & Business Media
ISBN: 9780792343905
Category : Mathematics
Languages : en
Pages : 424
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Book Description
This book is the result of many years of research in Non-Euclidean Geometries and Geometry of Lie groups, as well as teaching at Moscow State University (1947- 1949), Azerbaijan State University (Baku) (1950-1955), Kolomna Pedagogical Col lege (1955-1970), Moscow Pedagogical University (1971-1990), and Pennsylvania State University (1990-1995). My first books on Non-Euclidean Geometries and Geometry of Lie groups were written in Russian and published in Moscow: Non-Euclidean Geometries (1955) [Ro1] , Multidimensional Spaces (1966) [Ro2] , and Non-Euclidean Spaces (1969) [Ro3]. In [Ro1] I considered non-Euclidean geometries in the broad sense, as geometry of simple Lie groups, since classical non-Euclidean geometries, hyperbolic and elliptic, are geometries of simple Lie groups of classes Bn and D , and geometries of complex n and quaternionic Hermitian elliptic and hyperbolic spaces are geometries of simple Lie groups of classes An and en. [Ro1] contains an exposition of the geometry of classical real non-Euclidean spaces and their interpretations as hyperspheres with identified antipodal points in Euclidean or pseudo-Euclidean spaces, and in projective and conformal spaces. Numerous interpretations of various spaces different from our usual space allow us, like stereoscopic vision, to see many traits of these spaces absent in the usual space.
Author: Marjorie Senechal
Publisher: Nova Biomedical Books
ISBN:
Category : Mathematics
Languages : en
Pages : 110
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Book Description
Cultures of Science
Author: Robert J. Zimmer
Publisher: University of Chicago Press
ISBN: 022656813X
Category : Mathematics
Languages : en
Pages : 724
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Book Description
Robert J. Zimmer is best known in mathematics for the highly influential conjectures and program that bear his name. Group Actions in Ergodic Theory, Geometry, and Topology: Selected Papers brings together some of the most significant writings by Zimmer, which lay out his program and contextualize his work over the course of his career. Zimmer’s body of work is remarkable in that it involves methods from a variety of mathematical disciplines, such as Lie theory, differential geometry, ergodic theory and dynamical systems, arithmetic groups, and topology, and at the same time offers a unifying perspective. After arriving at the University of Chicago in 1977, Zimmer extended his earlier research on ergodic group actions to prove his cocycle superrigidity theorem which proved to be a pivotal point in articulating and developing his program. Zimmer’s ideas opened the door to many others, and they continue to be actively employed in many domains related to group actions in ergodic theory, geometry, and topology. In addition to the selected papers themselves, this volume opens with a foreword by David Fisher, Alexander Lubotzky, and Gregory Margulis, as well as a substantial introductory essay by Zimmer recounting the course of his career in mathematics. The volume closes with an afterword by Fisher on the most recent developments around the Zimmer program.
Author:
Publisher: Academic Press
ISBN: 0080873596
Category : Mathematics
Languages : en
Pages : 477
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Book Description
Introduction to Compact Transformation Groups
Author: Heinz J Rothe
Publisher: World Scientific
ISBN: 9814602302
Category :
Languages : en
Pages : 397
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Book Description
This book introduces a large number of topics in lattice gauge theories, including analytical as well as numerical methods. It provides young physicists with the theoretical background and basic computational tools in order to be able to follow the extensive literature on the subject, and to carry out research on their own. Whenever possible, the basic ideas and technical inputs are demonstrated in simple examples, so as to avoid diverting the readers' attention from the main line of thought. Sufficient technical details are however given so that he can fill in the remaining details with the help of the cited literature without too much effort.This volume is designed for graduate students in theoretical elementary particle physics or statistical mechanics with a basic knowledge in Quantum Field Theory.
Author: Benson Farb
Publisher: University of Chicago Press
ISBN: 0226237907
Category : Mathematics
Languages : en
Pages : 659
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Book Description
The study of group actions is more than a hundred years old but remains to this day a vibrant and widely studied topic in a variety of mathematic fields. A central development in the last fifty years is the phenomenon of rigidity, whereby one can classify actions of certain groups, such as lattices in semi-simple Lie groups. This provides a way to classify all possible symmetries of important spaces and all spaces admitting given symmetries. Paradigmatic results can be found in the seminal work of George Mostow, Gergory Margulis, and Robert J. Zimmer, among others. The papers in Geometry, Rigidity, and Group Actions explore the role of group actions and rigidity in several areas of mathematics, including ergodic theory, dynamics, geometry, topology, and the algebraic properties of representation varieties. In some cases, the dynamics of the possible group actions are the principal focus of inquiry. In other cases, the dynamics of group actions are a tool for proving theorems about algebra, geometry, or topology. This volume contains surveys of some of the main directions in the field, as well as research articles on topics of current interest.
Author: Robert J. Zimmer
Publisher: American Mathematical Soc.
ISBN: 0821883364
Category : Mathematics
Languages : en
Pages : 103
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Book Description
"The study of group actions on manifolds is the meeting ground of a variety of mathematical areas. In particular, interesting geometric insights can be obtained by applying measure-theoretic techniques. This book provides an introduction to some of the important methods, major developments, and open problems in the subject. It is slightly expanded from lectures given by Zimmer at the CBMS conference at the University of Minnesota. The main text presents a perspective on the field as it was at that time. Comments at the end of each chapter provide selected suggestions for further reading, including references to recent developments."--BOOK JACKET.
Author: J. M. Landsberg
Publisher: American Mathematical Soc.
ISBN: 0821869078
Category : Mathematics
Languages : en
Pages : 464
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Book Description
Tensors are ubiquitous in the sciences. The geometry of tensors is both a powerful tool for extracting information from data sets, and a beautiful subject in its own right. This book has three intended uses: a classroom textbook, a reference work for researchers in the sciences, and an account of classical and modern results in (aspects of) the theory that will be of interest to researchers in geometry. For classroom use, there is a modern introduction to multilinear algebra and to the geometry and representation theory needed to study tensors, including a large number of exercises. For researchers in the sciences, there is information on tensors in table format for easy reference and a summary of the state of the art in elementary language. This is the first book containing many classical results regarding tensors. Particular applications treated in the book include the complexity of matrix multiplication, P versus NP, signal processing, phylogenetics, and algebraic statistics. For geometers, there is material on secant varieties, G-varieties, spaces with finitely many orbits and how these objects arise in applications, discussions of numerous open questions in geometry arising in applications, and expositions of advanced topics such as the proof of the Alexander-Hirschowitz theorem and of the Weyman-Kempf method for computing syzygies.
