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07/12/2023
The next gap in the subrank of 3-tensors
Recent works of Costa-Dalai, Christandl-Gesmundo-Zuiddam, Blatter-Draism...
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04/20/2023
Geometry of Tensors: Open problems and research directions
This is a collection of open problems and research ideas following the p...
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12/28/2022
Partial Degeneration of Tensors
Tensors are often studied by introducing preorders such as restriction a...
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12/03/2022
A Gap in the Subrank of Tensors
The subrank of tensors is a measure of how much a tensor can be ”diagona...
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11/14/2022
Border complexity via elementary symmetric polynomials
In (ToCT'20) Kumar surprisingly proved that every polynomial can be appr...
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05/04/2022
Degree-restricted strength decompositions and algebraic branching programs
We analyze Kumar's recent quadratic algebraic branching program size low...
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08/30/2021
Algebraic compressed sensing
We introduce the broad subclass of algebraic compressed sensing problems...
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07/10/2020
Border rank non-additivity for higher order tensors
Whereas matrix rank is additive under direct sum, in 1981 Schönhage show...
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09/20/2019
Tensors with maximal symmetries
We classify tensors with maximal and next to maximal dimensional symmetr...
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09/10/2019
Kronecker powers of tensors and Strassen's laser method
We answer a question, posed implicitly by Coppersmith-Winogrand and Buer...
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11/13/2018