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About twenty years ago, Green wrote a survey article on the utility of looking at toy versions over finite fields of problems in additive combinatorics.
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2007
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2008
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B. Green and T. Tao, An inverse theorem for the Gowers U 3 ( G ) U^{3}(G) norm , Proc. Edinb. Math. Soc. (2) 51
2008
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2018
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D. Kazhdan and T. Ziegler, Approximate cohomology , Selecta Math. (N.S.) 24
2018
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R. Kleinberg, W. Sawin, and D. E. Speyer, The growth of tri-colored sum-free sets , Discrete Anal. (2018), Paper No. 12, 10. MR 3827120
2018
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F. Manners, Good bounds in certain systems of true complexity one , Discrete Anal. (2018), Paper No. 21, 40. MR 3900336
2018
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D. Král, O. Serra, and L. Vena, A combinatorial proof of the removal lemma for groups , J. Combin. Theory Ser. A 116
2009
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V. Bergelson, T. Tao, and T. Ziegler, An inverse theorem for the uniformity seminorms associated with the action of 𝔽 p ∞ \mathbb{F}^{\infty}_{p} , Geom. Funct. Anal. 19
2010
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E. Croot and O. Sisask, A probabilistic technique for finding almost-periods of convolutions , Geom. Funct. Anal. 20
2010
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W. T. Gowers and J. Wolf, The true complexity of a system of linear equations , Proc. Lond. Math. Soc. (3) 100
2010
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T. Tao and T. Ziegler, The inverse conjecture for the Gowers norm over finite fields via the correspondence principle , Anal. PDE 3
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2011
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B. Green, T. Tao, and T. Ziegler, An inverse theorem for the Gowers U 4 U^{4} -norm , Glasg. Math. J. 53
2011
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S. Peluse, Three-term polynomial progressions in subsets of finite fields , Israel J. Math. 228
2018
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K. Hosseini and S. Lovett, A bilinear Bogolyubov-Ruzsa lemma with polylogarithmic bounds , Discrete Anal. (2019), Paper No. 10, 14. MR 3975362
2019
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L. Milićević, Polynomial bound for partition rank in terms of analytic rank , Geom. Funct. Anal. 29
2019
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S. Norin, A distribution on triples with maximum entropy marginal , Forum Math. Sigma 7
2019
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D. Dong, X. Li, and W. Sawin, Improved estimates for polynomial Roth type theorems in finite fields , J. Anal. Math. 141
2020
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E. Naslund, Exponential bounds for the Erdős-Ginzburg-Ziv constant , J. Combin. Theory Ser. A 174
2020
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R. Han, M. T. Lacey, and F. Yang, A polynomial Roth theorem for corners in finite fields , Mathematika 67
2021
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B. Kuca, Further bounds in the polynomial Szemerédi theorem over finite fields , Acta Arith. 198
2021
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T. Schoen, Improved bound in Roth’s theorem on arithmetic progressions , Adv. Math. 386
2021
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D. Altman, On a conjecture of Gowers and Wolf , Discrete Anal. (2022), Paper No. 10, 13. MR 4481407
2022
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T. F. Bloom and J. Maynard, A new upper bound for sets with no square differences , Compos. Math. 158
2022
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2022
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2022
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2022
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J. Tidor, Quantitative bounds for the U 4 U^{4} -inverse theorem over low characteristic finite fields , Discrete Anal. (2022), Paper No. 14, 17. MR 4503221
2022
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F. Tyrrell, New lower bounds for cap sets , preprint (2022), arXiv:2209.10045
2022
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2023
Closest in time.
2023
Closest in time.
B. Green, F. Manners, and T. Tao, Sumsets and entropy revisited , preprint (2023), arXiv:2306.13403
2023
Closest in time.
Z. Kelley and R. Meka, Strong bounds for 3 3 -progressions , preprint (2023), arXiv:2302.05537
2023
Closest in time.
D. Kim, A. Li, and J. Tidor, Cubic Goldreich-Levin , Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), SIAM, Philadelphia, PA, 2023, pp. 4846–4892. MR 4538136
2023
Closest in time.