David Conlon

I am a Professor of Mathematics here at Caltech. For a full CV, see here. My email is dconlon@caltech.edu. My principal research interests are in combinatorics and number theory, particularly Ramsey theory, extremal graph theory, additive combinatorics, pseudorandomness and random graphs. See here for a list of current and former students. The notes for a short course in Ramsey theory may be found here. Notes for a course on extremal graph theory are here. Notes for a summer school on pseudorandom graphs are here. Here are some of my papers: Non-spherical sets versus lines in Euclidean Ramsey theory, with J. Führer, submitted. Hypergraphs accumulate, with B. Schülke, submitted. Around the positive graph conjecture, with J. Lee and L. Versteegen, submitted. A question of Erdős and Graham on Egyptian fractions, with J. Fox, X. He, D. Mubayi, H. T. Pham, A. Suk and J. Verstraëte, submitted. On off-diagonal hypergraph Ramsey numbers, with J. Fox, B. Gunby, X. He, D. Mubayi, A. Suk and J. Verstraëte, submitted. Big line or big convex polygon, with J. Fox, X. He, D. Mubayi, A. Suk and J. Verstraëte, submitted. Homogeneous structures in subset sums and non-averaging sets, with J. Fox and H. T. Pham, submitted. Simplicial Turán problems, with S. Piga and B. Schülke, submitted. Everywhere unbalanced configurations, with J. Lim, submitted. Subset sums, completeness and colorings, with J. Fox and H. T. Pham, submitted. Sums of linear transformations, with J. Lim, to appear in Trans. Amer. Math. Soc. Difference sets in ℝ^{d}, with J. Lim, to appear in Israel J. Math. Domination inequalities and dominating graphs, with J. Lee, to appear in Math. Proc. Cambridge Philos. Soc. Intervals in the Hales–Jewett theorem, with N. Kamčev, to appear in European J. Combin. Extremal numbers and Sidorenko's conjecture, with J. Lee and A. Sidorenko, Int. Math. Res. Not. 2024, 10285-10297. Ramsey numbers and the Zarankiewicz problem, with S. Mattheus, D. Mubayi and J. Verstraëte, Bull. London Math. Soc. 56 (2024), 2014-2023. Set-coloring Ramsey numbers and error-correcting codes near the zero-rate threshold, with J. Fox, H. T. Pham and Y. Zhao, IEEE Trans. Inform. Theory 70 (2024), 4074-4078. Set-coloring Ramsey numbers via codes, with J. Fox, X. He, D. Mubayi, A. Suk and J. Verstraëte, Studia Sci. Math. Hungar. 61 (2024), 1-15. Monochromatic components with many edges, with S. Luo and M. Tyomkyn, J. Combin. 15 (2024), 59-75. A new bound for the Brown–Erdős–Sós problem, with L. Gishboliner, Y. Levanzov and A. Shapira, J. Combin. Theory Ser. B. 158 (2023), 1-35. Sums of transcendental dilates, with J. Lim, Bull. London Math. Soc. 55 (2023), 2400-2406. Fixing a hole, with J. Lim, Discrete Comput. Geom. 70 (2023), 1551-1570. Hypergraph Ramsey numbers of cliques versus stars, with J. Fox, X. He, D. Mubayi, A. Suk and J. Verstraëte, Random Structures Algorithms 63 (2023), 610-623. Three early problems on size Ramsey numbers, with J. Fox and Y. Wigderson, Combinatorica 43 (2023), 743-768. On the size-Ramsey number of grids, with R. Nenadov and M. Trujić, Combin. Probab. Comput. 32 (2023), 874-880. Off-diagonal book Ramsey numbers, with J. Fox and Y. Wigderson, Combin. Probab. Comput. 32 (2023), 516-545. Ramsey numbers of trails and circuits, with M. Tyomkyn, J. Graph Theory 102 (2023), 194-196. Threshold Ramsey multiplicity for paths and even cycles, with J. Fox, B. Sudakov and F. Wei, European J. Combin. 107 (2023), 103612. More on lines in Euclidean Ramsey theory, with Y.-H. Wu, C. R. Math. Acad. Sci. Paris. 361 (2023), 897-901. Which graphs can be counted in C_{4}-free graphs?, with J. Fox, B. Sudakov and Y. Zhao, Pure Appl. Math. Q. 18 (2022), 2413-2432. Rational exponents near two, with O. Janzer, Adv. Comb. 2022, Paper No. 9, 10 pp. The upper logarithmic density of monochromatic subset sums, with J. Fox and H. T. Pham, Mathematika 68 (2022), 1292-1301. The size-Ramsey number of cubic graphs, with R. Nenadov and M. Trujić, Bull. London Math. Soc. 54 (2022), 2135-2150. Ramsey numbers of books and quasirandomness, with J. Fox and Y. Wigderson, Combinatorica 42 (2022), 309-363. Threshold Ramsey multiplicity for odd cycles, with J. Fox, B. Sudakov and F. Wei, Rev. Un. Mat. Argentina 64 (2022), 49-68. Some remarks on the Zarankiewicz problem, Math. Proc. Cambridge Philos. Soc. 173 (2022), 155-161. Monochromatic combinatorial lines of length three, Proc. Amer. Math. Soc. 150 (2022), 1-4. Lower bounds for multicolor Ramsey numbers, with A. Ferber, Adv. Math. 378 (2021), 107528. The regularity method for graphs with few 4-cycles, with J. Fox, B. Sudakov and Y. Zhao, J. London Math. Soc. 104 (2021), 2376-2401. Random multilinear maps and the Erdős box problem, with C. Pohoata and D. Zakharov, Discrete Anal. 2021, Paper No. 17, 8 pp. Sidorenko's conjecture for blow-ups, with J. Lee, Discrete Anal. 2021, Paper No. 2, 13 pp. On the extremal number of subdivisions, with J. Lee, Int. Math. Res. Not. 2021, 9122-9145. More on the extremal number of subdivisions, with O. Janzer and J. Lee, Combinatorica 41 (2021), 465-494. Extremal numbers of cycles revisited, Amer. Math. Monthly. 128 (2021), 464-466. Repeated patterns in proper colourings, with M. Tyomkyn, SIAM J. Discrete Math. 35 (2021), 2249-2264. Hypergraph expanders of all uniformities from Cayley graphs, with J. Tidor and Y. Zhao, Proc. London Math. Soc. 121 (2020), 1311-1336. Short proofs of some extremal results III, with J. Fox and B. Sudakov, Random Structures Algorithms 57 (2020), 958-982. Ramsey games near the critical threshold, with S. Das, J. Lee and T. Mészáros, Random Structures Algorithms 57 (2020), 940-957. Books versus triangles at the extremal density, with J. Fox and B. Sudakov, SIAM J. Discrete Math. 34 (2020), 385-398. The Ramsey number of books, Adv. Comb. 2019, Paper No. 3, 12 pp. Graphs with few paths of prescribed length between any two vertices, Bull. London Math. Soc. 51 (2019), 1015-1021. Online Ramsey numbers and the Subgraph Query Problem, with J. Fox, A. Grinshpun and X. He, in Building Bridges II, 159-194, Springer, 2019. Hypergraph cuts above the average, with J. Fox, M. Kwan and B. Sudakov, Israel J. Math. 233 (2019), 67-111. Hypergraph expanders from Cayley graphs, Israel J. Math. 233 (2019), 49-65. Lines in Euclidean Ramsey theory, with J. Fox, Discrete Comput. Geom. 61 (2019), 218-225. Tower-type bounds for unavoidable patterns in words, with J. Fox and B. Sudakov, Trans. Amer. Math. Soc. 372 (2019), 6213-6229. Rational exponents in extremal graph theory, with B. Bukh, J. Eur. Math. Soc. 20 (2018), 1747-1757. Some advances on Sidorenko's conjecture, with J. H. Kim, C. Lee and J. Lee, J. London Math. Soc. 98 (2018), 593-608. See here for a companion note. Quasirandomness in hypergraphs, with E. Aigner-Horev, H. Hàn, Y. Person and M. Schacht, Electron. J. Combin. (2018), P3.34. Hereditary quasirandomness without regularity, with J. Fox and B. Sudakov, Math. Proc. Cambridge Philos. Soc. 164 (2018), 385-399. Finite reflection groups and graph norms, with J. Lee, Adv. Math. 315 (2017), 130-165. Hedgehogs are not colour blind, with J. Fox and V. Rödl, J. Combin. 8 (2017), 475-485. Freiman homomorphisms on sparse random sets, with W. T. Gowers, Q. J. Math. 68 (2017), 275-300. Almost-spanning universality in random graphs, with A. Ferber, R. Nenadov and N. Škorić, Random Structures Algorithms 50 (2017), 380-393. Quasirandom Cayley graphs, with Y. Zhao, Discrete Anal. 2017, Paper No. 6, 14 pp. A sequence of triangle-free pseudorandom graphs, Combin. Probab. Comput. 26 (2017), 195-200. A note on induced Ramsey numbers, with D. Dellamonica Jr., S. La Fleur, V. Rödl and M. Schacht, in A Journey Through Discrete Mathematics, 357-366, Springer, 2017. Ordered Ramsey numbers, with J. Fox, C. Lee and B. Sudakov, J. Combin. Theory Ser. B. 122 (2017), 353-383. Combinatorial theorems in sparse random sets, with W. T. Gowers, Ann. of Math. 184 (2016), 367-454. Ramsey numbers of cubes versus cliques, with J. Fox, C. Lee and B. Sudakov, Combinatorica 36 (2016), 37-70. Short proofs of some extremal results II, with J. Fox and B. Sudakov, J. Combin. Theory Ser. B 121 (2016), 173-196. Monochromatic cycle partitions in local edge colourings, with M. Stein, J. Graph Theory 81 (2016), 134-145. A relative Szemerédi theorem, with J. Fox and Y. Zhao, Geom. Funct. Anal. 25 (2015), 733-762. See here for a companion note. The Erdős–Gyárfás problem on generalized Ramsey numbers, with J. Fox, C. Lee and B. Sudakov, Proc. London Math. Soc. 110 (2015), 1-18. On the grid Ramsey problem and related questions, with J. Fox, C. Lee and B. Sudakov, Int. Math. Res. Not. 17 (2015), 8052-8084. See here for a companion note. Recent developments in graph Ramsey theory, with J. Fox and B. Sudakov, Surveys in Combinatorics 2015, 49-118. Distinct volume subsets, with J. Fox, W. Gasarch, D. G. Harris, D. Ulrich and S. Zbarsky, SIAM J. Discrete Math. 29 (2015), 472-480. Combinatorial theorems relative to a random set, Proceedings of the International Congress of Mathematicians 2014, Vol. 4, 303-328. On the KŁR conjecture in random graphs, with W. T. Gowers, W. Samotij and M. Schacht, Israel J. Math. 203 (2014), 535-580. Extremal results in sparse pseudorandom graphs, with J. Fox and Y. Zhao, Adv. Math. 256 (2014), 206-290. The Green–Tao theorem: an exposition, with J. Fox and Y. Zhao, EMS Surv. Math. Sci. 1 (2014), 249-282. Cycle packing, with J. Fox and B. Sudakov, Random Structures Algorithms 45 (2014), 608-626. Short proofs of some extremal results, with J. Fox and B. Sudakov, Combin. Probab. Comput. 23 (2014), 8-28. Ramsey-type results for semi-algebraic relations, with J. Fox, J. Pach, B. Sudakov and A. Suk, Trans. Amer. Math. Soc. 366 (2014), 5043-5065. A preliminary version of this paper appeared in the Proceedings of the Twenty-ninth Annual Symposium on Computational Geometry, SoCG '13, Rio de Janeiro, Brazil, 309-318. Two extensions of Ramsey's theorem, with J. Fox and B. Sudakov, Duke Math. J. 162 (2013), 2903-2927. Graph removal lemmas, with J. Fox, Surveys in Combinatorics 2013, 1-50. The Ramsey number of dense graphs, Bull. London Math. Soc. 45 (2013), 483-496. An improved bound for the stepping-up lemma, with J. Fox and B. Sudakov, Discrete Appl. Math. 161 (2013), 1191-1196. Bounds for graph regularity and removal lemmas, with J. Fox, Geom. Funct. Anal. 22 (2012), 1191-1256. On two problems in graph Ramsey theory, with J. Fox and B. Sudakov, Combinatorica 32 (2012), 513-535. On the Ramsey multiplicity of complete graphs, Combinatorica 32 (2012), 171-186. Erdős–Hajnal-type theorems in hypergraphs, with J. Fox and B. Sudakov, J. Combin. Theory Ser. B 102 (2012), 1142-1154. Weak quasi-randomness for uniform hypergraphs, with H. Hàn, Y. Person and M. Schacht, Random Structures Algorithms 40 (2012), 1-38. Large almost monochromatic subsets in hypergraphs, with J. Fox and B. Sudakov, Israel J. Math. 181 (2011), 423-432. Hypergraph Ramsey numbers, with J. Fox and B. Sudakov, J. Amer. Math. Soc. 23 (2010), 247-266. An approximate version of Sidorenko's conjecture, with J. Fox and B. Sudakov, Geom. Funct. Anal. 20 (2010), 1354-1366. An extremal theorem in the hypercube, Electron. J. Combin. 17 (2010), R111. Erratum to this paper. A new upper bound for diagonal Ramsey numbers, Ann. of Math. 170 (2009), 941-960. Ramsey numbers of sparse hypergraphs, with J. Fox and B. Sudakov, Random Structures Algorithms 35 (2009), 1-14. On-line Ramsey numbers, SIAM J. Discrete Math. 23 (2009), 1954-1963. Hypergraph packing and sparse bipartite Ramsey numbers, Combin. Probab. Comput. 18 (2009), 913-923. A new upper bound for the bipartite Ramsey problem, J. Graph Theory 58 (2008), 351-356. On the existence of rainbow 4-term arithmetic progression, with V. Jungić and R. Radoičić, Graphs Combin. 23 (2007), 249-254. Rainbow solutions of linear equations over Zp, Discrete Math. 306 (2006), 2056-2063.