Towards a geometric approach to Strassen’s asymptotic rank conjecture

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Standard

Towards a geometric approach to Strassen’s asymptotic rank conjecture. / Conner, Austin; Gesmundo, Fulvio; Landsberg, Joseph M.; Ventura, Emanuele; Wang, Yao.

I: Collectanea Mathematica, Bind 72, Nr. 1, 2021, s. 63-86.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Conner, A, Gesmundo, F, Landsberg, JM, Ventura, E & Wang, Y 2021, 'Towards a geometric approach to Strassen’s asymptotic rank conjecture', Collectanea Mathematica, bind 72, nr. 1, s. 63-86. https://doi.org/10.1007/s13348-020-00280-8

APA

Conner, A., Gesmundo, F., Landsberg, J. M., Ventura, E., & Wang, Y. (2021). Towards a geometric approach to Strassen’s asymptotic rank conjecture. Collectanea Mathematica, 72(1), 63-86. https://doi.org/10.1007/s13348-020-00280-8

Vancouver

Conner A, Gesmundo F, Landsberg JM, Ventura E, Wang Y. Towards a geometric approach to Strassen’s asymptotic rank conjecture. Collectanea Mathematica. 2021;72(1):63-86. https://doi.org/10.1007/s13348-020-00280-8

Author

Conner, Austin ; Gesmundo, Fulvio ; Landsberg, Joseph M. ; Ventura, Emanuele ; Wang, Yao. / Towards a geometric approach to Strassen’s asymptotic rank conjecture. I: Collectanea Mathematica. 2021 ; Bind 72, Nr. 1. s. 63-86.

Bibtex

@article{26f64548c81f489d89e7bf59a6a3b229,
title = "Towards a geometric approach to Strassen{\textquoteright}s asymptotic rank conjecture",
abstract = "We make a first geometric study of three varieties in Cm⊗ Cm⊗ Cm (for each m), including the Zariski closure of the set of tight tensors, the tensors with continuous regular symmetry. Our motivation is to develop a geometric framework for Strassen{\textquoteright}s asymptotic rank conjecture that the asymptotic rank of any tight tensor is minimal. In particular, we determine the dimension of the set of tight tensors. We prove that this dimension equals the dimension of the set of oblique tensors, a less restrictive class introduced by Strassen.",
keywords = "Asymptotic rank, Matrix multiplication complexity, Slice rank, Tensor rank",
author = "Austin Conner and Fulvio Gesmundo and Landsberg, {Joseph M.} and Emanuele Ventura and Yao Wang",
year = "2021",
doi = "10.1007/s13348-020-00280-8",
language = "English",
volume = "72",
pages = "63--86",
journal = "Collectanea Mathematica",
issn = "0010-0757",
publisher = "Springer",
number = "1",

}

RIS

TY - JOUR

T1 - Towards a geometric approach to Strassen’s asymptotic rank conjecture

AU - Conner, Austin

AU - Gesmundo, Fulvio

AU - Landsberg, Joseph M.

AU - Ventura, Emanuele

AU - Wang, Yao

PY - 2021

Y1 - 2021

N2 - We make a first geometric study of three varieties in Cm⊗ Cm⊗ Cm (for each m), including the Zariski closure of the set of tight tensors, the tensors with continuous regular symmetry. Our motivation is to develop a geometric framework for Strassen’s asymptotic rank conjecture that the asymptotic rank of any tight tensor is minimal. In particular, we determine the dimension of the set of tight tensors. We prove that this dimension equals the dimension of the set of oblique tensors, a less restrictive class introduced by Strassen.

AB - We make a first geometric study of three varieties in Cm⊗ Cm⊗ Cm (for each m), including the Zariski closure of the set of tight tensors, the tensors with continuous regular symmetry. Our motivation is to develop a geometric framework for Strassen’s asymptotic rank conjecture that the asymptotic rank of any tight tensor is minimal. In particular, we determine the dimension of the set of tight tensors. We prove that this dimension equals the dimension of the set of oblique tensors, a less restrictive class introduced by Strassen.

KW - Asymptotic rank

KW - Matrix multiplication complexity

KW - Slice rank

KW - Tensor rank

UR - http://www.scopus.com/inward/record.url?scp=85079457610&partnerID=8YFLogxK

U2 - 10.1007/s13348-020-00280-8

DO - 10.1007/s13348-020-00280-8

M3 - Journal article

AN - SCOPUS:85079457610

VL - 72

SP - 63

EP - 86

JO - Collectanea Mathematica

JF - Collectanea Mathematica

SN - 0010-0757

IS - 1

ER -

ID: 243015707