- Periodicity
and decidability of translational tilings by rational polygonal
sets (with J. de Dios, J. Grebik, J. Madrid), to appear in the
Bent Fuglede memorial volume of Expositiones Mathematicae.

- On
integer distance sets (with M. Iliopoulou, S. Peluse),
preprint.

Quanta Magazine: Merging Fields, Mathematicians Go the Distance on Old Problem

- Undecidability
of translational monotilings (with T. Tao), to appear in the Journal of the
European Mathematical Society.

- Tiling,
spectrality and aperiodicity of connected sets (with M.
Kolountzakis), to appear in Israel Journal of Mathematics.

- A
counterexample to the periodic tiling conjecture (with T. Tao), Annals of Mathematics, 200 (2024),
301-363.
[arXiv]

Quanta Magazine: 'Nasty' Geometry Breaks Decades-Old Tiling Conjecture

- Measurable
tilings by abelian group actions (with J. Grebik, V. Rozhon, T.
Tao),
International Mathematics Research Notices (2023). [arXiv]

- Additive
energies on discrete cubes (with J. de Dios, P. Ivanisvili, J.
Madrid), Discrete Analysis 2023:13, 16 pp.

- Generalized
Collatz maps with almost bounded orbits (with F. Gonçalves, J.
Madrid), to appear in Indiana University Mathematics Journal.

- Undecidable
translational tilings with only two tiles, or one nonabelian tile (with T. Tao), Discrete &
Computational Geometry 70 (4), 1652-1706 (2023). [arXiv]

- An uncountable ergodic Roth
theorem and applications (with P. Durcik, A. Iseli, A.
Jamneshan, J. Madrid), Discrete and Continuous Dynamical Systems,
2022, 42 (11) 5509-5540. [arXiv]

- Decoupling
for fractal subsets of the parabola (with A. Chang, J. de Dios,
A. Jamneshan, Z. Li, J. Madrid), Mathematische Zeitschrift, 301,
1851-1879 (2022). [arXiv]

- The
structure of translational tilings in ℤᵈ (with T. Tao) Discrete
Analysis 2021:16, 28 pp.

- Spectrality
of product domains and Fuglede's conjecture for convex polytopes
(with N. Lev) Journal d'Analyse Mathematique, 140 (2020) 409-441. [arXiv]

- Fuglede's spectral
set conjecture for convex polytopes (with N. Lev) Analysis &
PDE, 10 (2017), 1497-1538. [arXiv]

- Spectrality
and tiling by cylindric domains (with N. Lev) Journal of
Functional Analysis, 271 (2016), 2808-2821. [arXiv]