Preprints

1. Local spectral gap and the Stuck–Zimmer conjecture, with Yuval Yifrach, arXiv 2026.

2. Applications of almost stationarity I: quantitative growth of injectivity radius and Stuck–Zimmer theorem, with Ilya Gekhtman, Omri Solan and Yuval Yifrach, arXiv 2026.

3. The structure of almost stationary measures, with Ilya Gekhtman, Omri Solan and Yuval Yifrach, arXiv 2026. 

4. ASL_n(Z) invariant random subsets of Z^n, with Mikołaj Frączyk, arXiv 2026.

5. On the structure of approximate rings, with Krzysztof Krupiński, arXiv 2026.

6. Quasihomomorphisms to real algebraic groups, joint with Sami Douba, Francesco Fournier-Facio and Sam Hughes, arXiv 2026.

7. Asymmetric stability for the Brunn–Minkowski inequality in compact Lie groups, arXiv 2025.

8. Minimal doubling for small subsets in compact Lie groups, arXiv 2024.

9. The structure of approximate lattices in linear groups, arXiv 2023, see this presentation.

10. The definitions of approximate lattices, arXiv 2023.

Publications

11. The non-ergodic Host-Kra-Ziegler structure theorem for Z^d-actions via measurable selections, joint with Asgar Jamneshan, accepted for publication at Transactions of the AMS, arXiv 2026.

12. Approximate lattices and S-adic linear groups, Transformation Groups 2026.

13. Small doubling for discrete subsets of non-commutative groups and a theorem of Lagarias, Ergodic Theory and Dynamical Systems 46 (2026), no. 3, 695–725. 

14. Maximal multiplicity of Laplacian eigenvalues in negatively curved surfaces, joint with Cyril Letrouit, Geometric and Functional Analysis 2024. 

15. Approximate lattices in higher-rank semi-simple groups, Geometric and Functional Analysis 2023.

16. Closed approximate subgroups: compactness, amenability and approximate lattices, Forum of Mathematics, Sigma 13 (2025), e5.

17. Infinite approximate subgroups of soluble Lie groups, Mathematische Annalen 2022. 

18. Approximate lattices and Meyer sets in nilpotent Lie groups, Discrete Analysis 2020. 

Other writings

• Language models as science tutors, ICML. Helped curate a database for testing capabilities and limitations of LLMs acting as tutors/study helpers at undergraduate level.

• Partial notes from a mini-course at the University of Warwick on recent developments in the study of approximate lattices, available here. The notes cover a short (4 pages) and essentially self-contained proof of a recent theorem of Hrushovski's on "quasi-models" for approximate groups. The only prerequisite is basic knowledge of the Stone-Cech compactification of a set.
  
  

• Approximate lattices: structure in linear groups, definition(s) and beyond, arXiv 2023, see this presentation. This is an earlier version of the papers "The structure of approximate lattices in linear groups", "The definitions of approximate lattices" and "Approximate lattices and S-adic linear groups". In addition to the content of these three papers, it contains a long introduction to approximate lattices and approximate subgroups, further structural results in greater generality, and a number of discussions and conjectures. 

• Appendix to "Foundations of geometric approximate groups theory" by M. Cordes, T. Hartnick and V. Tonić, 2022.