Publications

★ denotes selected papers

Submitted:

24) ★★ Improved dimension bounds for Falconer’s distance problem in the plane, with Alex Iosevich. 133 pages. Comment: The celebrated Falconer conjecture suffered a miserable death at the hands of OpenAI afterwards. OpenAI used OUR IDEAS to get their solution, even though we are not cited there.

23) Point configurations in Brownian traces, with Petr Kosenko, Juan Miguel Medina. 41 pages.

22) ★ The Erdős similarity conjecture and Rajchman measures, with Natalia Mora Cuellar (my trainee), Alex Iosevich, Neeraja Kulkarni (my trainee), Ignacio Rojas Aravena (my trainee). 28 pages.

21) Minkowski sums with convex curves without pointwise Fourier decay, with Alex Iosevich, Zhangze Li, Eyvindur Palsson, Krystal Taylor. 35 pages.

20) Arithmetic progressions in Cantor sets: admissible and forbidden scales, with Samantha Sandberg-Clark, Krystal Taylor. 33 pages.

19) ★ The Erdős similarity conjecture for two-fold sumsets with a geometric summand, with Natalia Mora Cuellar (my trainee), Alex Iosevich, Neeraja Kulkarni (my trainee), Ignacio Rojas Aravena (my trainee). 16 pages.

18) Joint ranges of additive and multiplicative densities along prescribed Folner sequences, with Natalia Mora Cuellar (my trainee), Ignacio Rojas Aravena (my trainee). 23 pages.

17) ★ Falconer lattice sets and the Erdős similarity problem, with Alex Iosevich. 37 pages.

16) PDE propagation, sampling, and the Fourier ratio, with Alex Iosevich, Joshua Iosevich, Eyvindur Palsson. 17 pages.

15) Discretization, sampling, and the Fourier ratio, with Alex Iosevich, Eyvindur Palsson. 22 pages.

14) ★ The Fourier ratio: uncertainty, restriction, and approximation for compactly supported measures, with Alex Iosevich, Zhihe Li (my trainee), Eyvindur Palsson. 38 pages.

13) Numbers omitting digits in certain base expansions, with Han Yu. 19 pages.

Published or accepted:

12) ★ Full measure universality for Cantor sets, with Pablo Shmerkin. Advances in Mathematics. 495 (2026), Paper No. 110978, 26 pp . 22 pages.

11) On the volumes of simplices determined by a subset of $\mathbb{R}^d$, with Pablo Shmerkin. Annales Fennici Mathematici, 50(1), 97–108. 2025. 12 pages.

10) ★ Thickness and a gap lemma in $\mathbb{R}^d$. International Mathematics Research Notices (IMRN). 2023, no. 19, 16453–16477. 19 pages.

9) A survey on Newhouse thickness, fractal intersections and patterns. Math. Comput. Appl. 2022, 27(6), 111. Proceedings of the conference honouring Karoly Simon’s 60th birthday. 22 pages.

8) Intersections of thick compact sets in $\mathbb{R}^d$, with Kenneth Falconer. Mathematische Zeitschrift.  301 (2022), no. 3, 2291–2315. 27 pages.

7) The density of sets containing large similar copies of finite sets, with Kenneth Falconer and Vjekoslav Kovač. Journal d’Analyse Mathématique 148 (2022), no. 1, 339–359. 19 pages.

6) An improved bound for the dimension of $(\alpha,2\alpha)$-Furstenberg sets, with Kornélia Héra and Pablo Shmerkin. Revista Matemática Iberoamericana.  38 (2022), no. 1, 295–322. 29 pages.

5) Improved bounds on the dimensions of sets that avoid approximate arithmetic progressions, with Jonathan Fraser and Pablo Shmerkin. Journal of Fourier Analysis and Applications. 27 (2021), no. 1, Paper No. 4, 14 pp. 14 pages.

4) Patterns in thick compact sets. Israel Journal of Mathematics.  244 (2021), no. 1, 95–126. 23 pages.

3) Large sets avoiding linear patterns. Proceedings of the American Mathematical Society. 149 (2021), no. 10, 4057–4066. 10 pages.

2) Small Sets containing any Pattern, with Ursula Molter. Math. Proc. Cambridge Philos. Soc. 168 (2020), no. 1, 57–73. 17 pages.

1) L^q dimensions and projections of random measures, with Daniel Galicer, Santiago Saglietti and Pablo Shmerkin. Nonlinearity 29 (2016), no. 9, 2609–2640. 32 pages.