Publications

★ denotes selected papers

Submitted:

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). 27 pages.

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

20) Arithmetic progressions in Cantor sets: admissible and forbidden scales, with Samantha Sandberg-Clark, Krystal Taylor. 33 pages. https://arxiv.org/abs/2608.14998

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. https://arxiv.org/abs/2607.03584 

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. https://arxiv.org/abs/2607.19525 

17) ★ Falconer lattice sets and the Erdős similarity problem, with Alex Iosevich. 37 pages. https://arxiv.org/html/2604.01493

16) PDE propagation, sampling, and the Fourier ratio, with Alex Iosevich, Joshua Iosevich, Eyvindur Palsson. 17 pages. https://arxiv.org/abs/2603.07851

15) Discretization, sampling, and the Fourier ratio, with Alex Iosevich, Eyvindur Palsson. 22 pages. https://arxiv.org/pdf/2601.17493

14) ★ The Fourier ratio: uncertainty, restriction, and approximation for compactly supported measures, with Alex Iosevich, Zhihe Li (my trainee), Eyvindur Palsson. 38 pages. arxiv.org/abs/2512.16751 

13) Numbers omitting digits in certain base expansions, with Han Yu. 19 pages. https://arxiv.org/abs/2503.09528

Published or accepted:

12) ★ Full measure universality for Cantor sets, with Pablo Shmerkin. Advances in Mathematics. 22 pages. http://arxiv.org/abs/2503.21079

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. https://arxiv.org/abs/2310.17855

10) ★ Thickness and a gap lemma in $\mathbb{R}^d$. International Mathematics Research Notices (IMRN). 2023, no. 19, 16453–16477. 19 pages. http://arxiv.org/abs/2204.08428

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. https://arxiv.org/abs/2212.02023

8) Intersections of thick compact sets in $\mathbb{R}^d$, with Kenneth Falconer. Mathematische Zeitschrift.  301 (2022), no. 3, 2291–2315. 27 pages. https://arxiv.org/abs/2102.01186

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. https://arxiv.org/abs/2007.03493

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 https://arxiv.org/abs/2001.11304

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. https://arxiv.org/abs/1910.10074

4) Patterns in thick compact sets. Israel Journal of Mathematics.  244 (2021), no. 1, 95–126. 23 pages. https://arxiv.org/abs/1910.10057

3) Large sets avoiding linear patterns. Proceedings of the American Mathematical Society. 149 (2021), no. 10, 4057–4066. 10 pages. https://arxiv.org/abs/1706.08118

2) Small Sets containing any Pattern, with Ursula Molter. Math. Proc. Cambridge Philos. Soc. 168 (2020), no. 1, 57–73. 17 pages. https://arxiv.org/abs/1610.03804

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. https://arxiv.org/abs/1504.04893