3 papers
math.GR2023
The definitions of approximate lattices
Simon Machado
Approximate lattices of locally compact groups were first studied in a seminal monograph of Yves Meyer and were subsequently used in the theory of aperiodic order to model objects…
math.NT2023
Approximate lattices and S-adic linear groups
Simon Machado
We provide and motivate in this paper a natural framework for the study of approximate lattices. Namely, we consider approximate lattices in so-called -adic linear groups and de…
math.GR2023
Small doubling for discrete subsets of non-commutative groups and a theorem of Lagarias
Simon Machado
Approximate lattices of Euclidean spaces, also known as Meyer sets, are aperiodic subsets with fascinating properties. In general, approximate lattices are defined as approximate s…