of translational monotilings (with T. Tao), preprint.
spectrality and aperiodicity of connected sets (with M.
counterexample to the periodic tiling conjecture (with T. Tao), preprint.
Quanta Magazine: 'Nasty'
Geometry Breaks Decades-Old Tiling Conjecture
tilings by abelian group actions (with J. Grebik, V. Rozhon, T.
International Mathematics Research Notices (2023). [arXiv]
energies on discrete cubes (with J. de Dios, P. Ivanisvili, J.
Madrid), Discrete Analysis 2023:13, 16 pp.
Collatz maps with almost bounded orbits (with F. Gonçalves, J.
Madrid), to appear in Indiana University Mathematics Journal.
translational tilings with only two tiles, or one nonabelian tile (with T. Tao), Discrete &
Computational Geometry (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]
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]
structure of translational tilings in ℤᵈ (with T. Tao) Discrete
Analysis 2021:16, 28 pp.
of product domains and Fuglede's conjecture for convex polytopes
(with N. Lev) Journal d'Analyse Mathematique, 140 (2020) 409-441. [arXiv]
spectral set conjecture for convex polytopes (with N. Lev)
Analysis & PDE, 10 (2017), 1497-1538. [arXiv]
and tiling by cylindric domains (with N. Lev) Journal of
Functional Analysis, 271 (2016), 2808-2821. [arXiv]