A geometric criterion on embedded disks along Teichmuller geodesics implies that for uniquely ergodic translation surfaces, almost every branched N-cover via a slit is uniquely ergodic.
The algebraic hull of the Kontsevich-Zorich cocycle
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We compute the algebraic hull of the Kontsevich-Zorich cocycle over any GL^+_2(R) invariant subvariety of the Hodge bundle, and derive from this finiteness results on such subvarieties.
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2026 1verdicts
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Unique ergodicity of branched covers of translation surfaces
A geometric criterion on embedded disks along Teichmuller geodesics implies that for uniquely ergodic translation surfaces, almost every branched N-cover via a slit is uniquely ergodic.