6 citations · 9 across the 9 of their papers we have counts for
10 papers
Applications of Almost Stationarity I: Quantitative Growth of Injectivity Radius and Stück-Zimmer Theorem
Ilya Gekhtman, Simon Machado, Omri Solan +1
Fraczyk and Gelander proved in \cite{FG} that for any simple Lie group of high rank and for every non-lattice discrete subgroup , the injectivity radius of points in $…
invariant random subsets of
Mikołaj Frączyk, Simon Machado
We classify measures on , , the space of subsets of , which are invariant under all affine special linear transformations. In other…
On the structure of approximate rings
Krzysztof Krupiński, Simon Machado
By a [-]approximate subring of a ring we mean an additively symmetric subset such that is covered by finitely many [resp.\ ] additive translates…
Maximal multiplicity of Laplacian eigenvalues in negatively curved surfaces
Cyril Letrouit, Simon Machado
In this work, we obtain the first upper bound on the multiplicity of Laplacian eigenvalues for negatively curved surfaces which is sublinear in the genus g. Our proof relies on a t…
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…