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Tensors Asymptotic Geometry And Developments 2016 2018
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Book Synopsis Tensors: Asymptotic Geometry and Developments 2016–2018 by : J.M. Landsberg
Download or read book Tensors: Asymptotic Geometry and Developments 2016–2018 written by J.M. Landsberg and published by American Mathematical Soc.. This book was released on 2019-07-05 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Applications of Polynomial Systems by : David A. Cox
Download or read book Applications of Polynomial Systems written by David A. Cox and published by American Mathematical Soc.. This book was released on 2020-03-02 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantum Computation and Quantum Information by : J. M. Landsberg
Download or read book Quantum Computation and Quantum Information written by J. M. Landsberg and published by American Mathematical Society. This book was released on 2024-06-28 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the basics of quantum computing and quantum information theory. It emphasizes the mathematical aspects and the historical continuity of both algorithms and information theory when passing from classical to quantum settings. The book begins with several classical algorithms relevant for quantum computing and of interest in their own right. The postulates of quantum mechanics are then presented as a generalization of classical probability. Complete, rigorous, and self-contained treatments of the algorithms of Shor, Simon, and Grover are given. Passing to quantum information theory, the author presents it as a straightforward adaptation of Shannon's foundations to information theory. Both Shannon's theory and its adaptation to the quantum setting are explained in detail. The book concludes with a chapter on the use of representation theory in quantum information theory. It shows how all known entropy inequalities, including the celebrated strong subadditivity of von Neumann entropy, may be obtained from a representation theory perspective. With many exercises in each chapter, the book is designed to be used as a textbook for a course in quantum computing and quantum information theory. Prerequisites are elementary undergraduate probability and undergraduate algebra, both linear and abstract. No prior knowledge of quantum mechanics or information theory is required.
Book Synopsis Fitting Smooth Functions to Data by : Charles Fefferman
Download or read book Fitting Smooth Functions to Data written by Charles Fefferman and published by American Mathematical Soc.. This book was released on 2020-10-27 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Tensors: Geometry and Applications by : J. M. Landsberg
Download or read book Tensors: Geometry and Applications written by J. M. Landsberg and published by American Mathematical Soc.. This book was released on 2011-12-14 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Tensor Valuations and Their Applications in Stochastic Geometry and Imaging by : Eva B. Vedel Jensen
Download or read book Tensor Valuations and Their Applications in Stochastic Geometry and Imaging written by Eva B. Vedel Jensen and published by Springer. This book was released on 2017-06-10 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Surveys on Recent Developments in Algebraic Geometry by : Izzet Coskun
Download or read book Surveys on Recent Developments in Algebraic Geometry written by Izzet Coskun and published by American Mathematical Soc.. This book was released on 2017-07-12 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: The algebraic geometry community has a tradition of running a summer research institute every ten years. During these influential meetings a large number of mathematicians from around the world convene to overview the developments of the past decade and to outline the most fundamental and far-reaching problems for the next. The meeting is preceded by a Bootcamp aimed at graduate students and young researchers. This volume collects ten surveys that grew out of the Bootcamp, held July 6–10, 2015, at University of Utah, Salt Lake City, Utah. These papers give succinct and thorough introductions to some of the most important and exciting developments in algebraic geometry in the last decade. Included are descriptions of the striking advances in the Minimal Model Program, moduli spaces, derived categories, Bridgeland stability, motivic homotopy theory, methods in characteristic and Hodge theory. Surveys contain many examples, exercises and open problems, which will make this volume an invaluable and enduring resource for researchers looking for new directions.
Book Synopsis Concepts from Tensor Analysis and Differential Geometry by : Tracy Y. Thomas
Download or read book Concepts from Tensor Analysis and Differential Geometry written by Tracy Y. Thomas and published by Elsevier. This book was released on 2016-06-03 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concepts from Tensor Analysis and Differential Geometry discusses coordinate manifolds, scalars, vectors, and tensors. The book explains some interesting formal properties of a skew-symmetric tensor and the curl of a vector in a coordinate manifold of three dimensions. It also explains Riemann spaces, affinely connected spaces, normal coordinates, and the general theory of extension. The book explores differential invariants, transformation groups, Euclidean metric space, and the Frenet formulae. The text describes curves in space, surfaces in space, mixed surfaces, space tensors, including the formulae of Gaus and Weingarten. It presents the equations of two scalars K and Q which can be defined over a regular surface S in a three dimensional Riemannian space R. In the equation, the scalar K, which is an intrinsic differential invariant of the surface S, is known as the total or Gaussian curvature and the scalar U is the mean curvature of the surface. The book also tackles families of parallel surfaces, developable surfaces, asymptotic lines, and orthogonal ennuples. The text is intended for a one-semester course for graduate students of pure mathematics, of applied mathematics covering subjects such as the theory of relativity, fluid mechanics, elasticity, and plasticity theory.
Book Synopsis Progress in Group Field Theory and Related Quantum Gravity Formalisms by : Steffen Gielen
Download or read book Progress in Group Field Theory and Related Quantum Gravity Formalisms written by Steffen Gielen and published by MDPI. This book was released on 2020-07-01 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Asymptotic Analysis in General Relativity by : Thierry Daudé
Download or read book Asymptotic Analysis in General Relativity written by Thierry Daudé and published by Cambridge University Press. This book was released on 2018-01-11 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume compiles notes from four mini courses given at the summer school on asymptotic analysis in general relativity, held at the Institut Fourier in Grenoble, France. It contains an up-to-date panorama of modern techniques in the asymptotic analysis of classical and quantum fields in general relativity. Accessible to graduate students, these notes gather results that were not previously available in textbooks or monographs and will be of wider interest to researchers in general relativity. The topics of these mini courses are: the geometry of black hole spacetimes; an introduction to quantum field theory on curved spacetimes; conformal geometry and tractor calculus; and microlocal analysis for wave propagation.
Book Synopsis Finsler Geometry, Relativity and Gauge Theories by : G.S. Asanov
Download or read book Finsler Geometry, Relativity and Gauge Theories written by G.S. Asanov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Tensor Geometry by : C. T. J. Dodson
Download or read book Tensor Geometry written by C. T. J. Dodson and published by . This book was released on 2014-01-15 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1976 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Progress and Trends in Rheology II by : H. Giesekus
Download or read book Progress and Trends in Rheology II written by H. Giesekus and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following an invitation from the Czechoslovakian The scientific programme consisted of 14 plenary delegates at the First Conference of European Rheo lectures as weIl as 310 short presentations, which were logists at Graz in 1982 and adecision by the European held in six parallel sessions in seven half-day sittings. members of the International Committee of Rheology The provision of a reading room containing submitted at the 1983 "Conference of Engineering Rheology" in manuscripts of talks presented at the meeting proved London, the Rheology Group of the Czechoslovak to be popular and seems a worthwhile addition to any Chemical Society (Chairman: Doz. lug. l. Sestak meeting, at least those holding parallel sessions. There CSc.) was entrusted with the organization of the Sec was also a display by nine companies of a wide variety ond Conference of European Rheologists. For an of current rheological instruments. outline of the process leading to the decision to hold The programme for accompanying persons befitted such European meetings, see the Introduction to the the historical significance of the region. The evening Proceedings of the First Conference of European programme included an opening ceremony and recep Rheologists; Rheol Acta 21:355-356 (1982). tion on Monday and an informal banquet on Thurs This Conference was held in the Prague Palace of day as weIl as a visit to the opera.
Author :Eduardo Bayro Corrochano Publisher :Springer Science & Business Media ISBN 13 :3540282475 Total Pages :773 pages Book Rating :4.5/5 (42 download)
Book Synopsis Handbook of Geometric Computing by : Eduardo Bayro Corrochano
Download or read book Handbook of Geometric Computing written by Eduardo Bayro Corrochano and published by Springer Science & Business Media. This book was released on 2005-12-06 with total page 773 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many computer scientists, engineers, applied mathematicians, and physicists use geometry theory and geometric computing methods in the design of perception-action systems, intelligent autonomous systems, and man-machine interfaces. This handbook brings together the most recent advances in the application of geometric computing for building such systems, with contributions from leading experts in the important fields of neuroscience, neural networks, image processing, pattern recognition, computer vision, uncertainty in geometric computations, conformal computational geometry, computer graphics and visualization, medical imagery, geometry and robotics, and reaching and motion planning. For the first time, the various methods are presented in a comprehensive, unified manner. This handbook is highly recommended for postgraduate students and researchers working on applications such as automated learning; geometric and fuzzy reasoning; human-like artificial vision; tele-operation; space maneuvering; haptics; rescue robots; man-machine interfaces; tele-immersion; computer- and robotics-aided neurosurgery or orthopedics; the assembly and design of humanoids; and systems for metalevel reasoning.
Book Synopsis Coarse Graining in Quantum Gravity: Bridging the Gap between Microscopic Models and Spacetime-Physics by : Astrid Eichhorn
Download or read book Coarse Graining in Quantum Gravity: Bridging the Gap between Microscopic Models and Spacetime-Physics written by Astrid Eichhorn and published by Frontiers Media SA. This book was released on 2021-07-15 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt:
