Full list of publications and submitted papers (listed in order of submission to arxiv)

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Convexity, elementary methods, and distances (joint with Dmitrii Zhelezov)

To appear in Discrete and Computational Geometry

Arxiv

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Large convex sets in difference sets (joint with Krishnendu Bhowmick and Ben Lund)

Submitted for publication

Arxiv

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Local differences determined by convex sets (joint with Krishnendu Bhowmick and Miriam Patry)

Integers 23, Paper no. A70, 11pp.

Arxiv      MathSciNet

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A better than 3/2 exponent for iterated sums and products

To appear in Mathematical Proceedings of the Cambridge Philosophical Society

Arxiv

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Counting arcs in F_q^2 (joint with Krishnendu Bhowmick)

To appear in Discrete and Computational Geometry

Arxiv

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A convex set with a rich difference (joint with Audie Warren)

Acta Mathematica Hungarica 168, no. 2 (2022), 587-592.

Arxiv      MathSciNet

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Convexity, Squeezing, and the Elekes-Szabó Theorem  (joint with Elaine Wong)

Electronic Journal of Combinatorics 31 (2024), no. 1, Paper No. 1.3, 23 pp.

Arxiv     MathSciNet

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Convexity, Superquadratic Growth, and Dot Products (joint with Brandon Hanson and Steven Senger)

Journal of the London Mathematical Society 107 (2023), 1900-1923.

Arxiv     MathSciNet

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Additive and multiplicative Sidon sets (joint with Audie Warren)

Acta Mathematica Hungarica 165, no. 2 (2021), 326-336.

Arxiv     MathSciNet

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Sums, products and dilates on sparse graphs

SIAM Journal on Discrete Mathematics 35(1) (2021), 194-204.

Arxiv     MathSciNet

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The Elekes-Szabó Problem and the Uniformity Conjecture (joint with Mehdi Makhul, Sophie Stevens and Audie Warren)

Israel Journal of Mathematics 248(1) (2022), 39-66.

Arxiv     MathSciNet

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Higher convexity and iterated sum sets (joint with Brandon Hanson and Misha Rudnev)

Combinatorica 42(1) (2022), 71-85.

Arxiv     MathSciNet

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Arcs in F_q^2 (joint with Audie Warren)

European Journal of Combinatorics 103 (2022), Paper No. 103512, 15 pp.

Arxiv     MathSciNet

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An energy bound in the affine group (joint with Giorgis Petridis, Misha Rudnev and Audie Warren)

International Mathematical Research Notices, Volume 2022, Issue 2, 1154-1172.

Arxiv     MathSciNet

 

Four-term progression free sets with three-term progressions in all large subsets (joint with Cosmin Pohoata)

Random Structures and Algorithms 60(4) (2022), 749-770.

Arxiv     MathSciNet

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New expander bounds from affine group energy (joint with Audie Warren)

Discrete and Computational Geometry 66 (2021), no. 2, 552-574.

Arxiv     MathSciNet

 

Constructions for the Elekes-Szabó and Elekes-Rónyai problems (joint with Mehdi Makhul, Audie Warren and Frank de Zeeuw)

Electronic Journal of Combinatorics 27 (2020), no. 1, Paper 1.57, 8pp.

Arxiv     MathSciNet

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An improved bound for the size of the set A/A+A 

Proceedings of the 34th International Symposium on Computational Geometry (2018), Article Number 69, 12 pp

Arxiv     MathSciNet

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If A+A is small then AAA is superquadratic (joint with Ilya Shkredov)

Journal of Number Theory 201 (2019), 124-134.

Arxiv     MathSciNet

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On iterated product sets with shifts II (joint with Brandon Hanson and Dmitrii Zhelezov)

Algebra and Number Theory 14 (2020), no. 8, 2239-2260.

Arxiv     MathSciNet

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Improved bounds for pencils of lines (joint with Audie Warren)

Proceedings of the American Mathematical Society 149 (2021), 805-815

Arxiv     MathSciNet

 

On the size of the set AA+A (joint with Imre Ruzsa, Chun-Yen Shen and Ilya Shkredov)

Journal of the London Mathematical Society 99 (2019), no. 2, 477-494

Arxiv     MathSciNet

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On iterated product sets with shifts (joint with Brandon Hanson and Dmitrii Zhelezov)

Mathematika 65 (2019), no. 4, 831-850

Arxiv     MathSciNet

 

Variations on the sum-product problem II (joint with Brendan Murphy and Ilya Shkredov)

SIAM Journal on Discrete Mathematics 31 (2017), no. 3, 1878-1894

Arxiv     MathSciNet

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Analogues of the Balog-Wooley decomposition for subsets of finite fields and character sums with convolutions (joint with Igor Shparlinski and Arne Winterhof)

Annals of Combinatorics 23 (2019), no. 1, 183-205

Arxiv     MathSciNet

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New results on sum-product type growth over fields (joint with Brendan Murphy, Giorgis Petridis, Misha Rudnev and Ilya Shkredov)

Mathematika 65 (2019), no. 3, 588-642

Arxiv     MathSciNet

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Expanders with superquadratic growth (joint with Antal Balog and Dmitrii Zhelezov)

Electronic Journal of Combinatorics 24 (2017), no. 3, Paper 3.14, 17 pp

Arxiv       MathSciNet

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Packing sets (joint with Ilya Shkredov and Arne Winterhof)

Integers 18 (2018), Paper No. A38, 9pp

Arxiv       MathSciNet

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On discrete values of bilinear forms (joint with Alex Iosevich and Misha Rudnev)

Sbornik:Mathematics 209 (2018), no. 10, 71-88. (Erratum for this paper)

Arxiv    MathSciNet

 

If (A+A)/(A+A) is small then the ratio set is large

Journal of the London Mathematical Society 93 (2016), 83-100

Arxiv    MathSciNet

 

A short proof of a near-optimal cardinality estimate for the product of a sum set

Proceedings of the 31st International Symposium on Computational Geometry (2015), 74-80

Arxiv       MathSciNet

 

On distinct perpendicular bisectors and pinned distances in finite fields (joint with Brandon Hanson and Ben Lund)

Finite Fields and Their Applications 37 (2016), 240-264

Arxiv       MathSciNet

 

Sets with few distinct distances do not have heavy lines (joint with Orit Raz and Micha Sharir)

Discrete Mathematics 338, (2015), 1484-1492

Arxiv    MathSciNet 

 

A bound on the multiplicative energy of a sum set and extremal sum-product problems (joint with Dmitrii Zhelezov)

Moscow Journal of Combinatorics and Number Theory 5(1-2) (2015), 53-70

Arxiv    MathSciNet

 

New sum-product type estimates over finite fields (joint with Misha Rudnev and Ilya Shkredov)

Advances in Mathematics 293 (2016), 589-605

Arxiv    MathSciNet

 

Elementary methods for incidence problems in finite fields (joint with Javier Cilleruelo, Alex Iosevich, Ben Lund and Misha Rudnev)

Acta Arithmetica 177(2) (2017), 133-142

Arxiv    MathSciNet

 

Polynomial values in subfields and affine subspaces of finite fields (joint with Igor Shparlinski)

Quarterly Journal of Mathematics 66(2) (2015), 693-706

Arxiv    MathSciNet 

 

New sum-product estimates for real and complex numbers (joint with Antal Balog)

Discrete and Computational Geometry 53(4) (2015), 825-846

Arxiv    MathSciNet 

 

Variations on the sum-product problem (joint with Brendan Murphy and Ilya Shkredov)

SIAM Journal on Discrete Mathematics 29(1) (2015), 514-540

Arxiv    MathSciNet

 

Improved bounds on the set A(A+1) (joint with Timothy G. F. Jones)

Journal of Combinatorial Theory, Series A 120(3) (2013), 515-526

Arxiv    MathSciNet

 

On the Minkowski distances and products of sum sets (joint with Misha Rudnev)

Israel Journal of Mathematics 209 (2015), 507-526

Arxiv       MathSciNet

 

Convexity and a sum-product type-estimate (joint Liangpan Li) 

Acta Arithmetica 156(3) (2012), 247-256

Arxiv    MathSciNet

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An improved sum-product estimate for general finite fields (joint with Liangpan Li)

SIAM Journal on Discrete Mathematics 25(3) (2011), 1285-1296

Arxiv    MathSciNet

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Other preprints (not intended for publication)

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On sets with few distinct distances

The main result of this paper was improved by Pohoata before it was published in a journal. I decided to withdraw the submission.

Arxiv  

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Sum-ratio estimates over arbitrary finite fields

This result (and its proof) is a variant of the main result (and its proof) in this paper. The result was needed for an application in this paper.

Arxiv  

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