On cap sets and the group-theoretic approach to matrix multiplication · Around

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On cap sets and the group-theoretic approach to matrix multiplication · Around

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J. B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers , Illinois J. Math. 6
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W. Hoeffding, Probability inequalities for sums of bounded random variables , J. Amer. Statist. Assoc. 58
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P. Erdős and E. Szemerédi, Combinatorial properties of systems of sets , J. Combinatorial Theory Ser. A 24
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A. Schönhage, Partial and total matrix multiplication , SIAM J. Comp. 10
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P. Bürgisser, M. Clausen, and M. A. Shokrollahi, Algebraic complexity theory , Grundlehren der Mathematischen Wissenschaften 315
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H. Cohn and C. Umans, A group-theoretic approach to fast matrix multiplication , Proceedings of the 44th Annual Symposium on Foundations of Computer Science, 11–14 October 2003, Cambridge, MA, IEEE Computer Society, pp. 438–449, arXiv: math.GR/0307321 , doi:10.1109/sfcs.2003.1238217
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H. Cohn, R. Kleinberg, B. Szegedy, and C. Umans, Group-theoretic algorithms for matrix multiplication , Proceedings of the 46th Annual Symposium on Foundations of Computer Science, 23–25 October 2005, Pittsburgh, PA, IEEE Computer Society, pp. 379–388, arXiv: math.GR/0511460 , doi:10.1109/sfcs.2005.39
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F. Le Gall, Powers of tensors and fast matrix multiplication , Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation, 23–25 July 2014, Kobe, Japan, Association for Computing Machinery, pp. 296–303, full version at arXiv: 1401.7714 , doi:10.1145/2608628.2608664
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2014
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R. Kleinberg, W. F. Sawin, and D. E. Speyer, The growth rate of tri-colored sum-free sets , preprint, 2016, arXiv: 1607.00047
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2016
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S. Norin, A distribution on triples with maximum entropy marginal , preprint, 2016, arXiv: 1608.00243
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L. Pebody, Proof of a conjecture of Kleinberg-Sawin-Speyer , preprint, 2016, arXiv: 1608.05740
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F. Petrov, Many zero divisors in a group ring imply bounds on progression-free subsets , preprint, 2016, arXiv: 1606.03256

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2011

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V. Vassilevska Williams, Multiplying matrices faster than Coppersmith–Winograd , Proceedings of the 44th ACM Symposium on Theory of Computing, 19–22 May 2012, New York, NY, Association for Computing Machinery, pp. 887–898, doi:10.1145/2213977.2214056

2012

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N. Alon, A. Shpilka, and C. Umans, On sunflowers and matrix multiplication , Computational Complexity 22

2013

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H. Cohn and C. Umans, Fast matrix multiplication using coherent configurations , Proceedings of the 24th Annual ACM-SIAM Symposium on Discrete Algorithms, 6–8 January 2013, New Orleans, LA, Society for Industrial and Applied Mathematics, pp. 1074–1087, arXiv: 1207.6528 , doi:10.1137/1.9781611973105.77

2013

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A. M. Davie and A. J. Stothers, Improved bound for complexity of matrix multiplication , Proc. Roy. Soc. Edinburgh Sect. A 143

2013

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2016

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T. Tao, A symmetric formulation of the Croot–Lev–Pach–Ellenberg–Gijswijt capset bound, blog post, 2016, http://terrytao.wordpress.com/2016/05/18/a

2016

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E. Croot, V. Lev, and P. Pach, Progression-free sets in ℤ 4 n {\mathbb{Z}}_{4}^{n} are exponentially small , Ann. of Math. (2) 185

2017

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J. S. Ellenberg and D. Gijswijt, On large subsets of 𝔽 q n {\mathbb{F}}_{q}^{n} with no three-term arithmetic progression , Ann. of Math. (2) 185

2017

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