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Tensors: Asymptotic Geometry and Developments 2016–2018
 
J.M. Landsberg Texas A&M University, College Station, TX
A co-publication of the AMS and CBMS
Tensors: Asymptotic Geometry and Developments 2016--2018
Softcover ISBN:  978-1-4704-5136-3
Product Code:  CBMS/132
List Price: $58.00
MAA Member Price: $52.20
AMS Member Price: $46.40
eBook ISBN:  978-1-4704-5291-9
Product Code:  CBMS/132.E
List Price: $58.00
MAA Member Price: $52.20
AMS Member Price: $46.40
Softcover ISBN:  978-1-4704-5136-3
eBook: ISBN:  978-1-4704-5291-9
Product Code:  CBMS/132.B
List Price: $116.00 $87.00
MAA Member Price: $104.40 $78.30
AMS Member Price: $92.80 $69.60
Tensors: Asymptotic Geometry and Developments 2016--2018
Click above image for expanded view
Tensors: Asymptotic Geometry and Developments 2016–2018
J.M. Landsberg Texas A&M University, College Station, TX
A co-publication of the AMS and CBMS
Softcover ISBN:  978-1-4704-5136-3
Product Code:  CBMS/132
List Price: $58.00
MAA Member Price: $52.20
AMS Member Price: $46.40
eBook ISBN:  978-1-4704-5291-9
Product Code:  CBMS/132.E
List Price: $58.00
MAA Member Price: $52.20
AMS Member Price: $46.40
Softcover ISBN:  978-1-4704-5136-3
eBook ISBN:  978-1-4704-5291-9
Product Code:  CBMS/132.B
List Price: $116.00 $87.00
MAA Member Price: $104.40 $78.30
AMS Member Price: $92.80 $69.60
  • Book Details
     
     
    CBMS Regional Conference Series in Mathematics
    Volume: 1322019; 144 pp
    MSC: Primary 68; 14; 15; 81

    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.

    Readership

    Undergraduate and graduate students and researchers interested in tensors, mathematical aspects of solid state physics, and quantum information theory.

  • Table of Contents
     
     
    • Basics
    • Motivation, first definitions and properties
    • Tensors via linear algebra
    • Rank and border rank
    • Tensor networks
    • The asymptotic geometry of tensors
    • Detour into probability and information theory
    • Strassen’s laser method and spectral theory
    • Quantum mechanics for quantum information theory
    • Quantum information theory and the asymptotic geometry of tensors
    • Moment maps and moment polytopes
    • Hints and answers to selected exercises
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 1322019; 144 pp
MSC: Primary 68; 14; 15; 81

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.

Readership

Undergraduate and graduate students and researchers interested in tensors, mathematical aspects of solid state physics, and quantum information theory.

  • Basics
  • Motivation, first definitions and properties
  • Tensors via linear algebra
  • Rank and border rank
  • Tensor networks
  • The asymptotic geometry of tensors
  • Detour into probability and information theory
  • Strassen’s laser method and spectral theory
  • Quantum mechanics for quantum information theory
  • Quantum information theory and the asymptotic geometry of tensors
  • Moment maps and moment polytopes
  • Hints and answers to selected exercises
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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