Pre-prints
Minimal doubling for small subsets in compact Lie groups, arXiv 2024.
The structure of approximate lattices in linear groups, arXiv 2023, see this presentation.
The definitions of approximate lattices, arXiv 2023.
Approximate lattices and S-adic linear groups, arXiv 2023.
Small doubling for discrete subsets of non-commutative groups and a theorem of Lagarias, arXiv 2023, see this presentation.
Publications
Maximal multiplicity of Laplacian eigenvalues in negatively curved surfaces, joint with Cyril Letrouit, Geometric and Functional Analysis 2024.
Approximate lattices in higher-rank semi-simple groups, Geometric and Functional Analysis 2023.
Closed approximate subgroups: compactness, amenability and approximate lattices, accepted for publication in Forum of Mathematics, Sigma 2024.
Infinite approximate subgroups of soluble Lie groups, Mathematische Annalen 2022.
Approximate lattices and Meyer sets in nilpotent Lie groups, Discrete Analysis 2020.
Other writings
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.