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Countable companions for Polish locally compact groups and their orbit equivalence relations
In "Countable sections for locally compact group actions" (Ergod. Th. & Dynam. Sys., 1992), Kechris proved that if $G$ is a Polish locally compact group acting in a Borel way on a ...
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Banach density of a sequence of spheres in a virtually nilpotent group
Let $G$ be a finitely-generated group of polynomial growth equipped with the word metric (with respect to a fixed symmetric generating set).
Let
\begin{equation*}
A = \left\{ g \in G: |g| = mn, n \...
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