# From topological recursion to wave functions and PDEs quantizing hyperelliptic curves

@article{Eynard2019FromTR, title={From topological recursion to wave functions and PDEs quantizing hyperelliptic curves}, author={Bertrand Eynard and Elba Garcia-Failde}, journal={arXiv: Mathematical Physics}, year={2019} }

Starting from loop equations, we prove that the wave functions constructed from topological recursion on families of spectral curves with a global involution satisfy a system of partial differential equations, whose equations can be seen as quantizations of the original spectral curves. The families of spectral curves can be parametrized with the so-called times, defined as periods on second type cycles. These equations can be used to prove that the WKB solution of many isomonodromic systems…

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