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 Mathematics 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.
Quantum Computation And Quantum Information
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Author : J. M. Landsberg
language : en
Publisher: American Mathematical Society
Release Date : 2024-06-28
Quantum Computation And Quantum Information written by J. M. Landsberg and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-28 with Mathematics categories.
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.
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.
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.
Rotational Integral Geometry And Its Applications
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Author : Eva B. Vedel Jensen
language : en
Publisher: Springer Nature
Release Date : 2025-07-14
Rotational Integral Geometry And Its Applications written by Eva B. Vedel Jensen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-14 with Mathematics categories.
This self-contained book offers an extensive state-of-the-art exposition of rotational integral geometry, a field that has reached significant maturity over the past four decades. Through a unified description of key results previously scattered across various scientific journals, this book provides a cohesive and thorough account of the subject. Initially, rotational integral geometry was driven by applications in fields such as optical microscopy. Rotational integral geometry has now evolved into an independent mathematical discipline. It contains a wealth of theorems paralleling those in classical kinematic integral geometry for Euclidean spaces, such as the rotational Crofton formulae, rotational slice formulae, and principal rotational formulae. The present book presents these for very general tensor valuations in a convex geometric setting. It also discusses various applications in the biosciences, explained with a mathematical audience in mind. This book is intended for a diverse readership, including specialists in integral geometry, and researchers and graduate students working in integral, convex, and stochastic geometry, as well as geometric measure theory.
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.
Surveys On Recent Developments In Algebraic Geometry
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Author : Izzet Coskun
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-07-12
Surveys On Recent Developments In Algebraic Geometry written by Izzet Coskun 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 2017-07-12 with Mathematics categories.
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.
Nuclear Science Abstracts
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Author :
language : en
Publisher:
Release Date : 1976
Nuclear Science Abstracts written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Nuclear energy categories.
Progress And Trends In Rheology Ii
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Author : P. Mitschka
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Progress And Trends In Rheology Ii written by P. Mitschka 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 2013-04-17 with Science categories.
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.