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arXiv · 2202.04400

$\hbar$-Riemann-Hilbert correspondence

Tatsuki Kuwagaki
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Abstract

We formulate and prove a Riemann-Hilbert correspondence between $\hbar$-differential equations and sheaf quantizations, which can be considered as a correspondence between two kinds of quantizations (deformation and sheaf quantization) of holomorphic cotangent bundles. The latter category is expected to be equivalent to a version of Fukaya category, which is a "quantization" of Lagrangian intersection theory. The ideas of the constructions are based on asymptotic/WKB analysis, which is related to geometric quantization.

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Tatsuki Kuwagaki. 2022-02-09. $\hbar$-Riemann-Hilbert correspondence. https://arxiv.org/abs/2202.04400

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