All of my preprints can be found in arxiv and ResearchGate.
Shamil Asgarli (10), Kübra Benli, Andries E. Brouwer, Alex Burgin, Cruz Castillo, Ting-Wei Chao, Xinbu Cheng, Ernie Croot (3),
Bence Csajbók, Michaela Cully-Hugill, Gabriel Currier (2), Alexei Entin, Dragos Ghioca (4), Xiang Gao (2), Gennian Ge,
Ritesh Goenka, Sergey Goryainov (4), Dominique Guillot (2), Himanshu Gupta (2), Seoyoung Kim (4), Greg Knapp, Jie Li,
Shuxing Li, Huiqiu Lin, Jonathan Love, Jewel Mahajan, Junzhe Mao, Greg Martin (4), Kenneth Moore (2), Yuveshen Mooroogen,
Nathan Ng, Pardis Semnani, Leonid Shalaginov (2), Jozsef Solymosi, Kin Ming Tsang, Prateek Kumar Vishwakarma (2),
Li-Yuan Wang, Meiqin Wang, Ethan White (3), Hai-Liang Wu, Zixiang Xu (5), Semin Yoo (5), Shengtong Zhang (2),
Xiaochen Zhao
[1] On the clique number of Paley graphs of prime power order. Finite Fields Appl. 77 (2022), Paper No. 101930, 16 pp. MR4320979. arXiv, journal [part of my master thesis]
[2] On the number of distinct roots of a lacunary polynomial over finite fields (with Jozsef Solymosi and Ethan White). Finite Fields Appl. 72 (2021), Paper No. 101820, 16 pp. MR4214976. arXiv, journal [part of my master thesis]
[3] On the directions determined by Cartesian products and the clique number of generalized Paley graphs. Integers 21 (2021), Paper No. A51, 31 pp. MR4256034. arxiv, journal (open access) [part of my master thesis]
[4] On maximal cliques of Cayley graphs over fields. J. Algebraic Combin. 56 (2022), no. 2, 323-333. MR4467957. arxiv, journal
[5] Gauss sums and the maximum cliques in generalized Paley graphs of square order. Funct. Approx. Comment. Math. 66 (2022), no. 1, 119-138. MR4397683. arxiv, journal
[6] Van Lint-MacWilliams' conjecture and maximum cliques in Cayley graphs over finite fields (with Shamil Asgarli). J. Combin. Theory Ser. A 192 (2022), Paper No. 105667, 23pp. MR4457404. arxiv, journal
[7] Asymptotics for the number of directions determined by [n]*[n] in Fp^2 (with Greg Martin and Ethan White). Mathematika 68 (2022), no. 2, 511-534. MR4418456. arxiv, journal, pdf
[8] The subspace structure of maximum cliques in pseudo-Paley graphs from unions of cyclotomic classes (with Shamil Asgarli). Finite Fields Appl. 99 (2024), Paper No. 102492, 36 pp. MR4785288. arXiv, journal
[9] The EKR-module property of pseudo-Paley graphs of square order (with Shamil Asgarli, Sergey Goryainov, and Huiqiu Lin). Electron. J. Combin. 29 (2022), no. 4, Paper No. 4.33, 19 pp. MR4516936. arXiv, journal (open access)
[10] On eigenfunctions and maximal cliques of generalised Paley graphs of square order (with Sergey Goryainov and Leonid Shalaginov). Finite Fields Appl. 87 (2023), Paper No. 102150, 36 pp. MR4531528. arxiv, journal
[11] Intersective sets over abelian groups (with Zixiang Xu). Submitted, arxiv
[12] Plane curves giving rise to blocking sets over finite fields (with Shamil Asgarli and Dragos Ghioca). Des. Codes Cryptogr. 91 (2023), no. 11, 3643–3669. MR4659423. arxiv, journal
[13] Maximality of subfields as cliques in Cayley graphs over finite fields. Algebr. Comb. 6 (2023), no. 4, 901-905. MR4635081. arxiv, journal (open access)
[14] Sperner systems with restricted differences (with Zixiang Xu). Comb. Theory., to appear. arxiv
[15] Most plane curves over finite fields are not blocking (with Shamil Asgarli and Dragos Ghioca). J. Combin. Theory Ser. A 204 (2024), Paper No. 105871, 26pp. MR4703360. arxiv, journal (open access)
[16] Proportion of blocking curves in a pencil (with Shamil Asgarli and Dragos Ghioca). Discrete Math. 349 (2026), no. 1, Paper No. 114668, 7pp. MR4927522. arxiv, journal
[17] Existence of pencils with nonblocking hypersurfaces (with Shamil Asgarli and Dragos Ghioca). Finite Fields Appl. 92 (2023), Paper No. 102283, 11 pp. MR4632692. arxiv, journal
[18] Erdős-Ko-Rado theorem in Peisert-type graphs. Canad. Math. Bull. 67 (2024), no.1, 176-187. MR4706809. arxiv, journal (open access)
[19] Exact values and improved bounds on k-neighborly families of boxes (with Xinbu Cheng, Meiqin Wang and Zixiang Xu). European J. Combin. 118 (2024), Paper No. 103926, 17pp. MR4691751. arxiv, journal
[20] Additive decompositions of large multiplicative subgroups in finite fields. Acta Arith. 213 (2024), no.2, 97-116. MR4742652. arxiv, journal
[21] An exponential bound for simultaneous embeddings of planar graphs (with Ritesh Goenka and Pardis Semnani). Graphs Combin. 39 (2023), no. 5, Paper No. 100, 9 pp. MR4628948. arxiv, journal
[22] Exact values and improved bounds on the clique number of cyclotomic graphs. Under revision, arxiv
[23] Extremal Peisert-type graphs without the strict-EKR property (with Sergey Goryainov). J. Combin. Theory Ser. A 206 (2024), Paper No. 105887, 42pp. MR4719893. arxiv, journal
[24] Explicit constructions of Diophantine tuples over finite fields (with Seoyoung Kim and Semin Yoo). Ramanujan J. 65 (2024), no. 1, 163-172. MR4789393. arxiv, journal (open access)
[25] Multiplicative structure of shifted multiplicative subgroups and its applications to Diophantine tuples (with Seoyoung Kim and Semin Yoo). Canad. J. Math., to appear. arxiv, journal (open access) [part of my PhD thesis]
[26] Restricted sumsets in multiplicative subgroups. Canad. J. Math., to appear. arxiv, journal (open access) [part of my PhD thesis]
[27] On an Erdős similarity problem in the large (with Xiang Gao and Yuveshen Mooroogen). Bull. Lond. Math. Soc. 57 (2025), no. 6, 1801-1818. MR4917775. arxiv, journal (open access) [part of my PhD thesis]
[28] Multiplicatively reducible subsets of shifted perfect k-th powers and bipartite Diophantine tuples. Acta Arith. 218 (2025), no.3, 251-271. MR4889098. arxiv, journal [part of my PhD thesis]
[29] Any two-coloring of the plane contains monochromatic 3-term arithmetic progressions (with Gabriel Currier and Kenneth Moore). Combinatorica 44 (2024), no. 6, 1367-1380. MR4826642. arxiv, journal, extended abstract in conference proceeding
[30] Distribution of power residues over shifted subfields and maximal cliques in generalized Paley graphs (with Greg Martin). Proc. Amer. Math. Soc. 153 (2025), no. 1, 109-124. MR4840262. arxiv, journal, pdf
[31] Mutual position of two smooth quadrics over finite fields (with Shamil Asgarli). Des. Codes Cryptogr., to appear. arxiv, journal (open access)
[32] On cyclotomic matrices involving Gauss sums over finite fields (with Jie Li, Li-Yuan Wang, and Hai-Liang Wu). Proc. Amer. Math. Soc. 153 (2025), no. 4, 1411-1424. MR4868954. arxiv, journal
[33] Avoiding short progressions in Euclidean Ramsey theory (with Gabriel Currier and Kenneth Moore). J. Combin. Theory Ser. A 217 (2026), Paper No. 106080, 17pp. MR4919810. arxiv, journal (open access)
[34] Paley-like quasi-random graphs arising from polynomials (with Seoyoung Kim and Semin Yoo). Submitted, arxiv
[35] F-Diophantine sets over finite fields (with Semin Yoo). Int. J. Number Theory 21 (2025), no. 5, 1043-1050. MR4903958. arxiv, journal (open access)
[36] Improved upper bounds on Diophantine tuples with the property D(n). Bull. Aust. Math. Soc. 111 (2025), no. 3, 428-432. MR4903208. arxiv, journal (open access)
[37] A strengthening of McConnel's theorem on permutations over finite fields. Canad. Math. Bull. 68 (2025), no. 1, 213-218. MR4862236. arxiv, journal
[38] An Annotated Bibliography for Comparative Prime Number Theory (with Greg Martin, Pu Justin Scarfy Yang, Aram Bahrini, Prajeet Bajpai, Kübra Benli, Jenna Downey, Yuan Yuan Li, Xiaoxuan Liang, Amir Parvardi, Reginald Simpson, and Ethan White). Expo. Math. 43 (2025), no. 3, Paper No. 125644, 124 pp. MR4870699. arxiv, journal (open access)
[39] On the fractional parts of certain sequences of ξα^n (with Xiang Gao). Submitted, arxiv
[40] Upper bounds on polynomial root separation (with Greg Knapp). Bull. Aust. Math. Soc., to appear. arxiv, journal (open access)
[41] Positivity preservers over finite fields (with Dominique Guillot, Himanshu Gupta, and Prateek Kumar Vishwakarma). J. Algebra 684 (2025), 479-523. MR4941160. arxiv, journal. (Extended abstract in proceedings of FPSAC 2025: Sém. Lothar. Combin. 93B (2025) , Art. 69, 12 pp. journal )
[42] Oscillation results for the summatory functions of fake mu's (with Greg Martin). Canad. J. Math., to appear. arxiv
[43] The Frankl-Pach upper bound is not tight for any uniformity (with Gennian Ge, Zixiang Xu, Shengtong Zhang, and Xiaochen Zhao). J. Combin. Theory Ser. A 217 (2026), Paper No. 106078, 9pp. MR4916840. arxiv, journal
[44] Hypersurfaces passing through the Galois orbit of a point (with Shamil Asgarli and Jonathan Love). Submitted, arxiv
[45] Uniform set systems with small VC-dimension (with Ting-Wei Chao, Zixiang Xu, and Shengtong Zhang). Under revision, arxiv, blog by Ting-Wei Chao (in Chinese)
[46] Multiplicative irreducibility of small perturbations of shifted k-th powers. Submitted, arxiv
[47] Cliques in Paley graphs of square order and in Peisert graphs (with Andries E. Brouwer, Sergey Goryainov, and Leonid Shalaginov). Submitted, arxiv
[48] Quasi-random hypergraphs arising from multivariate polynomials and their applications to Diophantine sets (with Seoyoung Kim and Semin Yoo). Submitted, arxiv
[49] Diophantine tuples and product sets in shifted powers (with Ernie Croot). Submitted, arxiv
[50] Van Lint--MacWilliams' conjecture and maximum cliques in Cayley graphs over finite fields, II. Submitted, arxiv
[51] Entrywise transforms preserving matrix positivity and non-positivity (with Dominique Guillot, Himanshu Gupta, and Prateek Kumar Vishwakarma). Submitted, arxiv