4 problems

Glasner–Huang–Shao–Weiss–Ye polynomial odd-recurrence conjecture
Glasner–Huang–Shao–Weiss–Ye conjecture. The set $R$ has nonempty intersection with every infinite arithmetic progression of step size $k$ .
openFrom papersminimal-systems recurrence topological-dynamics
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6
Conjecture on finite-to-one maximal equicontinuous factors of minimal actions
Let $G$ be an amenable group, ${G \curvearrowright X}$ a minimal action, and let $k\geq 2$ . Write ${\rm IT}_k(X,G)$ for the set of independence tuples of length $k$ , let…
openFrom papersamenable-groups minimal-systems topological-dynamics
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6
The pro-nilfactor conjecture for topological characteristic factors along arithmetic progressions
Pro-nilfactor conjecture. If $(X,T)$ is a distal minimal system, then its maximal $(d-1)$ -step pro-nilfactor is its topological characteristic factor along arithmetic progressions…
openFrom papersminimal-systems nilfactors topological-dynamics
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5
Infinitely many minimal subsystems in universal symbolic systems
A universal symbolic system is a symbolic dynamical system capable of simulating every effective symbolic system. Universality conjecture. Every universal symbolic system has infin…
openFrom papersminimal-systems subshifts symbolic-dynamics
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4

Glasner–Huang–Shao–Weiss–Ye polynomial odd-recurrence conjecture