# 2-Parameter $$\tau$$-Function for the First Painlevé Equation: Topological Recursion and Direct Monodromy Problem via Exact WKB Analysis

@article{Iwaki20202Parameter,
title={2-Parameter \$\$\tau \$\$-Function for the First Painlev{\'e} Equation: Topological Recursion and Direct Monodromy Problem via Exact WKB Analysis},
author={Kohei Iwaki},
journal={Communications in Mathematical Physics},
year={2020},
volume={377},
pages={1047-1098}
}
• Kohei Iwaki
• Published 18 February 2019
• Mathematics
• Communications in Mathematical Physics
We show that a 2-parameter family of $$\tau$$ -functions for the first Painleve equation can be constructed by the discrete Fourier transform of the topological recursion partition function for a family of elliptic curves. We also perform an exact WKB theoretic computation of the Stokes multipliers of associated isomonodromy system assuming certain conjectures.
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