3 problems

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Persistence conjecture for Kontsevich-Zorich monodromy
Persistence conjecture. This behaviour persists in all genera.
Conjectureopenkontsevich-zorich-cocycle monodromy-groups origamisarXiv posted 2 days ago
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Forni–Zorich–Matheus conjecture on zero Lyapunov exponents and monodromy
Consider the Kontsevich–Zorich cocycle and its monodromy group on an irreducible piece of the relevant Hodge bundle over a moduli space of translation surfaces. Forni–Zorich–Matheu…
Conjectureopenkontsevich-zorich-cocycle lyapunov-exponents monodromyarXiv posted 2 days ago
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Forni's converse conjecture on non-uniform hyperbolicity of the KZ cocycle
Let $\mu$ be an $SL(2,\mathbb{R})$ -invariant probability measure on a moduli space of translation surfaces, and consider the Kontsevich–Zorich cocycle over $\mu$ . A translation sur…
Conjectureopenkontsevich-zorich-cocycle lyapunov-exponents translation-surfacesarXiv posted 2 days ago

Persistence conjecture for Kontsevich-Zorich monodromy