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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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06/02/2023
Discreteness of asymptotic tensor ranks
Tensor parameters that are amortized or regularized over large tensor po...
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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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05/30/2022
Subrank and Optimal Reduction of Scalar Multiplications to Generic Tensors
Since the seminal works of Strassen and Valiant it has been a central th...
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11/16/2021
Larger Corner-Free Sets from Combinatorial Degenerations
There is a large and important collection of Ramsey-type combinatorial p...
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04/02/2021
Communication Complexity, Corner-Free Sets and the Symmetric Subrank of Tensors
We develop and apply new combinatorial and algebraic tools to understand...
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12/28/2020
Weighted Slice Rank and a Minimax Correspondence to Strassen's Spectra
Structural and computational understanding of tensors is the driving for...
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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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03/06/2020
Barriers for rectangular matrix multiplication
We study the algorithmic problem of multiplying large matrices that are ...
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02/21/2020
Geometric rank of tensors and subrank of matrix multiplication
Motivated by problems in algebraic complexity theory (e.g., matrix multi...
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05/08/2019
The asymptotic induced matching number of hypergraphs: balanced binary strings
We compute the asymptotic induced matching number of the k-partite k-uni...
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12/17/2018
Barriers for fast matrix multiplication from irreversibility
The determination of the asymptotic algebraic complexity of matrix multi...
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10/01/2018
Quantum asymptotic spectra of graphs and non-commutative graphs, and quantum Shannon capacities
We study several quantum versions of the Shannon capacity of graphs and ...
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06/30/2018
The asymptotic spectrum of graphs and the Shannon capacity
We introduce the asymptotic spectrum of graphs and apply the theory of a...
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09/22/2017