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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Geometry and the complexity of matrix multiplication
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by J. M. Landsberg PDF
Bull. Amer. Math. Soc. 45 (2008), 247-284 Request permission

Abstract:

We survey results in algebraic complexity theory, focusing on matrix multiplication. Our goals are (i) to show how open questions in algebraic complexity theory are naturally posed as questions in geometry and representation theory, (ii) to motivate researchers to work on these questions, and (iii) to point out relations with more general problems in geometry. The key geometric objects for our study are the secant varieties of Segre varieties. We explain how these varieties are also useful for algebraic statistics, the study of phylogenetic invariants, and quantum computing.
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Additional Information
  • J. M. Landsberg
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
  • MR Author ID: 288424
  • Email: jml@math.tamu.edu
  • Received by editor(s): November 17, 2006
  • Received by editor(s) in revised form: March 12, 2007
  • Published electronically: January 7, 2008
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Bull. Amer. Math. Soc. 45 (2008), 247-284
  • MSC (2000): Primary 68Q17
  • DOI: https://doi.org/10.1090/S0273-0979-08-01176-2
  • MathSciNet review: 2383305