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Tensors: Asymptotic Geometry and Developments 2016-2018 (Paperback)
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Tensors: Asymptotic Geometry and Developments 2016-2018 (Paperback)
Series: CBMS Regional Conference Series in Mathematics
Expected to ship within 12 - 19 working days
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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.
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