3 problems

Weak containment and conjugate subgroups of the Bohr compactification
Let $G$ be a finitely generated group. Let $G \curvearrowright^\pi \mathcal{H}$ be an orthogonal representation, and let $G \curvearrowright^{\pi'} \mathcal{H}'$ be an irreducible…
openFrom papersbohr-compactification orthogonal-representations weak-containment
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6
The commutativity conjecture for the identity component of a pseudofinite group's Bohr compactification
Commutativity conjecture. If $G$ is a pseudofinite group, then $(bG)^{0}$ is commutative.
openFrom papersbohr-compactification compact-groups pseudofinite-groups
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4
Bourgain's conjecture for trigonometric polynomials on the Bohr compactification of $\mathbb R$
Bourgain's conjecture in the Bohr compactification. For any increasing sequence $(\omega_j)_{j\in\mathbb N}$ of real numbers,
openFrom papersbohr-compactification harmonic-analysis polynomials
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3

Weak containment and conjugate subgroups of the Bohr compactification