Rank of a median algebra equals the independence number of its median-preserving functions, and finite-rank compact median algebras are always Rosenthal representable (hence dynamically tame).
Coulembier: Algebraic geometry in tensor categories
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Proves the conjecture that higher Verlinde categories are geometrically reductive and reduces two further conjectures on geometric reductivity to other conjectures in the literature.
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Tameness of actions on finite rank median algebras
Rank of a median algebra equals the independence number of its median-preserving functions, and finite-rank compact median algebras are always Rosenthal representable (hence dynamically tame).
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On geometrically reductive tensor categories
Proves the conjecture that higher Verlinde categories are geometrically reductive and reduces two further conjectures on geometric reductivity to other conjectures in the literature.