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06/26/2023
On Linear spaces of of matrices bounded rank
Motivated by questions in theoretical computer science and quantum infor...
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05/11/2022
Concise tensors of minimal border rank
We determine defining equations for the set of concise tensors of minima...
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08/13/2021
Algebraic Geometry and Representation theory in the study of matrix multiplication complexity and other problems in theoretical computer science
Many fundamental questions in theoretical computer science are naturally...
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12/08/2020
On the geometry of geometric rank
We make a geometric study of the Geometric Rank of tensors recently intr...
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09/23/2020
Bad and good news for Strassen's laser method: Border rank of the 3x3 permanent and strict submultiplicativity
We determine the border ranks of tensors that could potentially advance ...
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12/26/2019
Towards finding hay in a haystack: explicit tensors of border rank greater than 2.02m in C^m⊗ C^m⊗ C^m
We write down an explicit sequence of tensors in C^m⊗ C^m⊗ C^m, for all ...
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11/18/2019
New lower bounds for matrix multiplication and the 3x3 determinant
Let M_〈 u,v,w〉∈ C^uv⊗ C^vw⊗ C^wu denote the matrix multiplication tensor...
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01/02/2018