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math.DS2024
A Szemerédi type theorem for sets of positive density in approximate lattices
Michael Björklund, Alexander Fish
An extension of Szemerédi's Theorem is proved for sets of positive density in approximate lattices in general locally compact and second countable abelian groups. As a consequence,…
math.DS2024★ 1 cited
Simplices in large sets and directional expansion in ergodic actions
Michael Björklund, Alexander Fish
In this paper we study ergodic -actions and investigate expansion properties along cyclic subgroups. We show that under some spectral conditions there are always dire…