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Caltech
Dylan King

Dylan King Homepage

Welcome to my website. I am a fourth year math graduate student at Caltech working for David Conlon. In the past few years I've been at the University of Bristol (working for David Ellis) and Part III of the Mathematical Tripos at the University Cambridge. I generally work in extremal combinatorics and am happy studying discrete phenomena involving (hyper)graphs, colorings, or forbidden structures.

I will be graduating in June 2027 and applying for postdoctoral positions in autumn 2026.


If you would like more details than this website offers, here is a copy of my CV. You are also welcome to contact me at [email protected].

Publications:

  • King, D., Lidický, B., Ouyang, M., Pfender, F., Wang, R., & Xiang, Z. (2025). On Relative Ordered Turán Density. (submitted). arXiv:2508.05515
  • King, D., Piga, S., Sales, M., & Schülke, B. (2025). On possible uniform Turán densities. (submitted). arXiv:2504.21220
  • Crawford, N., King, D., & Spiro, S. (2025). Rainbow Erdős–Sós Conjectures. (submitted). arXiv:2502.00135
  • King, D., Sales, M., & Schülke, B. (2024). Lagrangians are attained as uniform Turán densities. (to appear in Israel Journal of Mathematics). arXiv:2412.07297
  • Heath, E., King, D., McCourt, G., Sheats, H., & Wisby, J. (2024). Online Ramsey numbers of ordered graphs. (submitted). arXiv:2409.01917
  • Ellis, D., & King, D. (2023). Lower bounds for the Turán densities of daisies. Electronic Journal of Combinatorics, 30(4). arXiv:2204.08930
  • Fish, S., King, D., & Miller, S. J. (2020). Extensions of Autocorrelation Inequalities with Applications to Additive Combinatorics. Bulletin of the Australian Mathematical Society, 102(3), 451–461. arXiv:2001.02326
  • Coen, F., Gillman, N., Keleti, T., King, D. A., & Zhu, J. (2021). Large Sets with Small Injective Projections. Annales Fennici Mathematici, 46(2), 683–702. arXiv:1906.06288
  • King, D. A., Martinez, T., Miller, S. J., & Sun, C. (2022). Generalizing the Distribution of Missing Sums in Sumsets. Journal of Number Theory, 239, 402–444. arXiv:2005.07981
  • Fish, S., King, D. A., Miller, S. J., & Wahlenmayer, C. G. (2019). Crescent Configurations in Normed Spaces. Integers, 20, A96. arXiv:1909.08769
  • Fang, S., King, D., Lee, E. B., & Strichartz, R. (2019). Spectral decimation for families of self-similar symmetric Laplacians on the Sierpiński gasket. Journal of Fractal Geometry, 7(1), 1–62. arXiv:1709.02031