Towards finding hay in a haystack: explicit tensors of border rank greater than 2.02m in ℂ^m ⊗ ℂ^m ⊗ ℂ^m

Joseph Landsberg and Mateusz Michałek

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Submission date: 02. Jan. 2020
Bibtex
MSC-Numbers: 15A69, 14L35, 68Q15
Link to arXiv: See the arXiv entry of this preprint.

Abstract:
We write down an explicit sequence of tensors in ℂ^m ⊗ ℂ^m ⊗ ℂ^m, for all m sufficiently large, having border rank at least 2.02m, overcoming a longstanding barrier. We obtain our lower bounds via the border substitution method.