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تسجيل مستخدم جديدQuantization of hyper-elliptic curves from isomonodromic systems and topological recursion
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We prove that the topological recursion formalism can be used to compute the WKB expansion of solutions of second order differential operators obtained by quantization of any hyper-elliptic curve. We express this quantum curve in terms of spectral Darboux coordinates on the moduli space of meromorphic $mathfrak{sl}_2$-connections on $mathbb{P}^1$ and argue that the topological recursion produces a $2g$-parameter family of associated tau functions, where $2g$ is the dimension of the moduli space considered. We apply this procedure to the 6 Painleve equations which correspond to $g=1$ and consider a $g=2$ example.
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