We prove three results concerning the existence of Bohr sets in threefold sumsets. More
precisely, letting G be a countable discrete abelian group and be commuting …

We prove that there is a set of integers $ A $ having positive upper Banach density whose
difference set $ AA:=\{ab: a, b\in A\} $ does not contain a Bohr neighborhood of any integer …

Katznelson's Question is a long-standing open question concerning recurrence in
topological dynamics with strong historical and mathematical ties to open problems in …

We construct a set of integers produces a rigidity sequence. This construction generalizes or
strengthens results of Katznelson, Saeki (on equidistribution and the Bohr topology), Forrest …

We answer a question of Hegyvári and Ruzsa concerning effective estimates of the Bohr-
regularity of certain triple sums of sets with positive upper Banach densities in the integers …

If $ A $ is a set of integers having positive upper Banach density and $ r, s, t $ are nonzero
integers whose sum is zero, a theorem of Bergelson and Ruzsa says that the set $ rA+ sA+ …

We study pairs of subsets $ A, B $ of a compact abelian group $ G $ where the sumset $ A+
B:=\{a+ b: a\in A, b\in B\} $ is small. Let $ m $ and $ m_ {*} $ be Haar measure and inner …

Let $ G $ be a compact abelian group and $\phi_1,\phi_2,\phi_3 $ be continuous
endomorphisms on $ G $. Under certain natural assumptions on the $\phi_i $'s, we prove …

For a fixed prime $ p $, $\mathbb F_ {p} $ denotes the field with $ p $ elements, and
$\mathbb F_ {p}^{\omega} $ denotes the countable direct sum $\bigoplus_ {n …

We collect problems on recurrence for measure preserving and topological actions of a
countable abelian group, considering combinatorial versions of these problems as well. We …