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Subrank and optimal reduction of scalar multiplications to generic tensors

https://doi.org/10.1112/jlms.12963

Derksen, Harm ; Makam, Visu ; Zuiddam, Jeroen ( August 2024 , Journal of the London Mathematical Society)

The subrank of a tensor measures how much a tensor can be diagonalized. We determine this parameter precisely for essentially all (i.e., generic) tensors.
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Free, publicly-accessible full text available August 1, 2025
Invariant Theory and wheeled PROPs

https://doi.org/10.1016/j.jpaa.2022.107302

Derksen, Harm ; Makam, Visu ( September 2023 , Journal of Pure and Applied Algebra)

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Ranks of linear matrix pencils separate simultaneous similarity orbits

https://doi.org/10.1016/j.aim.2023.108888

Derksen, Harm ; Klep, Igor ; Makam, Visu ; Volčič, Jurij ( February 2023 , Advances in Mathematics)

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Polystability in positive characteristic and degree lower bounds for invariant rings

https://doi.org/10.4171/JCA/66

Derksen, Harm ; Makam, Visu ( January 2022 , Journal of Combinatorial Algebra)

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On the tensor rank of the 3 x 3 permanent and determinant

https://doi.org/10.13001/ela.2021.5107

Krishna, Siddharth ; Makam, Visu ( January 2021 , The Electronic Journal of Linear Algebra)
null (Ed.)
The tensor rank and border rank of the $3 \times 3$ determinant tensor are known to be $5$ if the characteristic is not two. In characteristic two, the existing proofs of both the upper and lower bounds fail. In this paper, we show that the tensor rank remains $5$ for fields of characteristic two as well.
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Maximum Likelihood Estimation for Matrix Normal Models via Quiver Representations

https://doi.org/10.1137/20M1369348

Derksen, Harm ; Makam, Visu ( January 2021 , SIAM Journal on Applied Algebra and Geometry)
null (Ed.)
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An exponential lower bound for the degrees of invariants of cubic forms and tensor actions

https://doi.org/10.1016/j.aim.2020.107136

Derksen, Harm ; Makam, Visu ( July 2020 , Advances in Mathematics)

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The regularity lemma is false over small fields

https://doi.org/10.1080/00927872.2019.1684507

Derksen, Harm ; Makam, Visu ( March 2020 , Communications in Algebra)

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Highly entangled tensors

https://doi.org/10.1080/03081087.2020.1726276

Derksen, Harm ; Makam, Visu ( January 2020 , Linear and Multilinear Algebra)

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Algorithms for orbit closure separation for invariants and semi-invariants of matrices

https://doi.org/10.2140/ant.2020.14.2791

Derksen, Harm ; Makam, Visu ( January 2020 , Algebra & Number Theory)
null (Ed.)
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