Hub-and-spoke systems from symbolic dynamics can have completely positive mean dimension without uniformly positive mean dimension or entropy, with proofs linking entropy and mean dimension properties at the level of fixed covers.
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Conjecture that simple geodesics on finite modular covers have transcendental or algebraic endpoints, proved for minimal laminations.
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Uniformly Positive Mean Dimension
Hub-and-spoke systems from symbolic dynamics can have completely positive mean dimension without uniformly positive mean dimension or entropy, with proofs linking entropy and mean dimension properties at the level of fixed covers.
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Transcendence of simple geodesics on finite modular covers
Conjecture that simple geodesics on finite modular covers have transcendental or algebraic endpoints, proved for minimal laminations.