Tensors Asymptotic Geometry And Developments 2016 2018
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Tensors Asymptotic Geometry And Developments 2016 2018
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Author : J.M. Landsberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-07-05
Tensors Asymptotic Geometry And Developments 2016 2018 written by J.M. Landsberg 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 2019-07-05 with Calculus of tensors categories.
Tensors are used throughout the sciences, especially in solid state physics and quantum information theory. This book brings a geometric perspective to the use of tensors in these areas. It begins with an introduction to the geometry of tensors and provides geometric expositions of the basics of quantum information theory, Strassen's laser method for matrix multiplication, and moment maps in algebraic geometry. It also details several exciting recent developments regarding tensors in general. In particular, it discusses and explains the following material previously only available in the original research papers: (1) Shitov's 2017 refutation of longstanding conjectures of Strassen on rank additivity and Common on symmetric rank; (2) The 2017 Christandl-Vrana-Zuiddam quantum spectral points that bring together quantum information theory, the asymptotic geometry of tensors, matrix multiplication complexity, and moment polytopes in geometric invariant theory; (3) the use of representation theory in quantum information theory, including the solution of the quantum marginal problem; (4) the use of tensor network states in solid state physics, and (5) recent geometric paths towards upper bounds for the complexity of matrix multiplication. Numerous open problems appropriate for graduate students and post-docs are included throughout.
Applications Of Polynomial Systems
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Author : David A. Cox
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-03-02
Applications Of Polynomial Systems written by David A. Cox 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 2020-03-02 with Education categories.
Systems of polynomial equations can be used to model an astonishing variety of phenomena. This book explores the geometry and algebra of such systems and includes numerous applications. The book begins with elimination theory from Newton to the twenty-first century and then discusses the interaction between algebraic geometry and numerical computations, a subject now called numerical algebraic geometry. The final three chapters discuss applications to geometric modeling, rigidity theory, and chemical reaction networks in detail. Each chapter ends with a section written by a leading expert. Examples in the book include oil wells, HIV infection, phylogenetic models, four-bar mechanisms, border rank, font design, Stewart-Gough platforms, rigidity of edge graphs, Gaussian graphical models, geometric constraint systems, and enzymatic cascades. The reader will encounter geometric objects such as Bézier patches, Cayley-Menger varieties, and toric varieties; and algebraic objects such as resultants, Rees algebras, approximation complexes, matroids, and toric ideals. Two important subthemes that appear in multiple chapters are toric varieties and algebraic statistics. The book also discusses the history of elimination theory, including its near elimination in the middle of the twentieth century. The main goal is to inspire the reader to learn about the topics covered in the book. With this in mind, the book has an extensive bibliography containing over 350 books and papers.
Fitting Smooth Functions To Data
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Author : Charles Fefferman
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-10-27
Fitting Smooth Functions To Data written by Charles Fefferman 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 2020-10-27 with Education categories.
This book is an introductory text that charts the recent developments in the area of Whitney-type extension problems and the mathematical aspects of interpolation of data. It provides a detailed tour of a new and active area of mathematical research. In each section, the authors focus on a different key insight in the theory. The book motivates the more technical aspects of the theory through a set of illustrative examples. The results include the solution of Whitney's problem, an efficient algorithm for a finite version, and analogues for Hölder and Sobolev spaces in place of Cm. The target audience consists of graduate students and junior faculty in mathematics and computer science who are familiar with point set topology, as well as measure and integration theory. The book is based on lectures presented at the CBMS regional workshop held at the University of Texas at Austin in the summer of 2019.
Tensor Valuations And Their Applications In Stochastic Geometry And Imaging
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Author : Eva B. Vedel Jensen
language : en
Publisher: Springer
Release Date : 2017-06-10
Tensor Valuations And Their Applications In Stochastic Geometry And Imaging written by Eva B. Vedel Jensen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-10 with Mathematics categories.
The purpose of this volume is to give an up-to-date introduction to tensor valuations and their applications. Starting with classical results concerning scalar-valued valuations on the families of convex bodies and convex polytopes, it proceeds to the modern theory of tensor valuations. Product and Fourier-type transforms are introduced and various integral formulae are derived. New and well-known results are presented, together with generalizations in several directions, including extensions to the non-Euclidean setting and to non-convex sets. A variety of applications of tensor valuations to models in stochastic geometry, to local stereology and to imaging are also discussed.
Tensors
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Author : J. M. Landsberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Tensors written by J. M. Landsberg 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.
Progress In Group Field Theory And Related Quantum Gravity Formalisms
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Author : Steffen Gielen
language : en
Publisher: MDPI
Release Date : 2020-07-01
Progress In Group Field Theory And Related Quantum Gravity Formalisms written by Steffen Gielen and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-01 with Mathematics categories.
Following the fundamental insights from quantum mechanics and general relativity, geometry itself should have a quantum description; the search for a complete understanding of this description is what drives the field of quantum gravity. Group field theory is an ambitious framework in which theories of quantum geometry are formulated, incorporating successful ideas from the fields of matrix models, ten-sor models, spin foam models and loop quantum gravity, as well as from the broader areas of quantum field theory and mathematical physics. This special issue collects recent work in group field theory and these related approaches, as well as other neighbouring fields (e.g., cosmology, quantum information and quantum foundations, statistical physics) to the extent that these are directly relevant to quantum gravity research.
Tensor Operators And Their Applications
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Author : Arif Salimov
language : en
Publisher: Nova Science Publishers
Release Date : 2013
Tensor Operators And Their Applications written by Arif Salimov and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Tensor algebra categories.
The notion of derivation of tensor fields is one of the central concepts and tools of mathematics. The author believes that differential geometric applications of tensor operators is a very fruitful research domain and provides many new problems in the study of modern differential geometry. This book is intended to provide a systematic introduction to the theory of tensor operators. This book is suitable for researchers, and will complement the Mathematics Research Developments Series, which will focus on research-level monographs. This book will also serve as a useful classroom resource for graduate students as well as final year undergraduate students on geometry, algebra, topology and physics.
Finsler Geometry Relativity And Gauge Theories
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Author : G.S. Asanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Finsler Geometry Relativity And Gauge Theories written by G.S. Asanov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The methods of differential geometry have been so completely merged nowadays with physical concepts that general relativity may well be considered to be a physical theory of the geometrical properties of space-time. The general relativity principles together with the recent development of Finsler geometry as a metric generalization of Riemannian geometry justify the attempt to systematize the basic techniques for extending general relativity on the basis of Finsler geometry. It is this endeavour that forms the subject matter of the present book. Our exposition reveals the remarkable fact that the Finslerian approach is automatically permeated with the idea of the unification of the geometrical space-time picture with gauge field theory - a circumstance that we try our best to elucidate in this book. The book has been written in such a way that the reader acquainted with the methods of tensor calculus and linear algebra at the graduate level can use it as a manual of Finslerian techniques orientable to applications in several fields. The problems attached to the chapters are also intended to serve this purpose. This notwithstanding, whenever we touch upon the Finslerian refinement or generalization of physical concepts, we assume that the reader is acquainted with these concepts at least at the level of the standard textbooks, to which we refer him or her.
Asymptotic Analysis In General Relativity
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Author : Thierry Daudé
language : en
Publisher: Cambridge University Press
Release Date : 2018-01-11
Asymptotic Analysis In General Relativity written by Thierry Daudé and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-11 with Mathematics categories.
Introduction to modern methods for classical and quantum fields in general relativity / Thierry Daudé, Dietrich Häfner, and Jean-Philippe Nicolas -- Geometry of black hole spacetimes / Lars Andersson, Thomas B. Ackdahl, and Pieter Blue -- An introduction to Quantum Field Theory on curved space-times / Christian Gerard -- A minicourse on microlocal analysis for wave propagation / Andras Vasy -- An introduction to conformal geometry and tractor calculus, with a view to applications in general relativity / Sean N. Curry and A. Rod Gover
Tensors
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Author : J. M. Landsberg
language : en
Publisher:
Release Date : 2011
Tensors written by J. M. Landsberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Matrices categories.