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The Cohn-Umans group-theoretic approach to matrix multiplication suggests embedding matrix multiplication into group algebra multiplication, and bounding $\omega$ in terms of the representation theory of the host group.
The structure of the group ring of a p p -group over a modular field
S. A. Jennings · 1941
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On spaces of linear transformations with bounded rank
H. Flanders · 1962
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Approximate formulas for some functions of prime numbers
J. B. Rosser and L. Schoenfeld · 1962
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On the associated graded ring of a group ring
D. G. Quillen · 1968
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Partial and total matrix multiplication
A. Schönhage · 1981
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Matrix multiplication via arithmetic progressions
D. Coppersmith and S. Winograd · 1990
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Algebraic complexity theory
P. Bürgisser, M. Clausen, and M. A. Shokrollahi · 1997
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A group-theoretic approach to fast matrix multiplication
H. Cohn and C. Umans · 2003
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Group-theoretic algorithms for matrix multiplication
H. Cohn, R. Kleinberg, B. Szegedy, and C. Umans · 2005
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On the complexity of matrix multiplication
A. Stothers · 2010
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Multiplying matrices faster than Coppersmith–Winograd
V. Vassilevska Williams · 2012
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On sunflowers and matrix multiplication
N. Alon, A. Shpilka, and C. Umans · 2013
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Improved lower bounds for testing triangle-freeness in Boolean functions via fast matrix multiplication
H. Fu and R. Kleinberg · 2014
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Powers of tensors and fast matrix multiplication
F. Le Gall · 2014
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Fast matrix multiplication: Limitations of the Coppersmith–Winograd method
A. Ambainis, Y. Filmus, and F. Le Gall · 2015
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A connection between matchings and removal in abelian groups
J. Aaronson · 2016
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Combinatorial results implied by many zero divisors in a group ring
F. Petrov · 2016
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A symmetric formulation of the Croot–Lev–Pach–Ellenberg–Gijswijt capset bound
T. Tao · 2016
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Notes on the “slice rank” of tensors
T. Tao and W. F. Sawin · 2016
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On cap sets and the group-theoretic approach to matrix multiplication
J. Blasiak, T. Church, H. Cohn, J. A. Grochow, E. Naslund, W. F. Sawin, and C. Umans · 2017
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Progression-free sets in ℤ 4 n \mathbb{Z}^{n}_{4} are exponentially small
E. Croot, V. F. Lev, and P. P. Pach · 2017
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J. S. Ellenberg · 2016
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Rank counting and maximum subsets of 𝔽 q n \mathbb{F}_{q}^{n} containing no right angles
G. Ge and C. Shangguan · 2016
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The growth rate of tri-colored sum-free sets
R. Kleinberg, W. F. Sawin, and D. E. Speyer · 2016
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A distribution on triples with maximum entropy marginal
S. Norin · 2016
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Upper bounds for sunflower-free sets
E. Naslund and W. F. Sawin · 2016
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Proof of a conjecture of Kleinberg–Sawin–Speyer
L. Pebody · 2016
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Z. Dvir and B. Edelman · 2017
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On large subsets of 𝔽 q n \mathbb{F}^{n}_{q} with no three-term arithmetic progression
J. S. Ellenberg and D. Gijswijt · 2017
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A tight bound for Green’s arithmetic triangle removal lemma in vector spaces
J. Fox and L. M. Lovász · 2017
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Sárközy’s theorem in function fields
B. Green · 2017
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An upper bound on tricolored ordered sum-free sets
T. Kim and S. Oum · 2017
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Bounds for matchings in nonabelian groups
W. F. Sawin · 2017
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