6 citations · 9 across the 9 of their papers we have counts for
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The structure of approximate lattices in linear groups
Simon Machado
Approximate lattices are aperiodic generalisations of lattices of locally compact groups that were first studied in seminal work of Yves Meyer. They are defined as those uniformly…
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…
Approximate Lattices in Higher-Rank Semi-Simple Groups
Simon Machado
We show that strong approximate lattices in higher-rank semi-simple algebraic groups are arithmetic.
Closed approximate subgroups: compactness, amenability and approximate lattices
Simon Machado
We investigate properties of closed approximate subgroups of locally compact groups, with a particular interest for approximate lattices i.e. those approximate subgroups that are d…
Infinite Approximate Subgroups of Soluble Lie Groups
Simon Machado
We study infinite approximate subgroups of soluble Lie groups. Generalising a theorem of Fried and Goldman we show that approximate subgroups are close, in a sense to be defined, t…
Approximate Lattices and Meyer Sets in Nilpotent Lie Groups
Simon Machado
We show that uniform approximate lattices in nilpotent Lie groups are subsets of model sets. This extends a theorem due to Yves Meyer about quasicrystals in Euclidean spaces. To do…