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In arXiv:1805.10945, arXiv:1810.02946, arXiv:2005.08957 the free energy of topological recursion is shown to satisfy differential/difference equations for some specially chosen curves.

Are there other cases when the free energy of topological recursion satisfies a differential or difference equation?

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    $\begingroup$ I am just learning about these topics, but if you're considering the setting where $L\cdot e^F=0$ where $L$ is a differential operator (Airy structure) in some Weyl algebra (with possibly infinitely many variables), then expanding that equation will inevitably lead to non-linear PDEs satisfied by the free energy $F$. $\endgroup$
    – Pedro
    Commented Jun 8, 2021 at 9:48
  • $\begingroup$ Are you sure about the ag.algebraic-geometry tag? Seems a bit far away! $\endgroup$
    – Evgeny Shinder
    Commented Jun 8, 2021 at 16:19

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