A sheaf quantization is a sheaf associated to a Lagrangian brane. This sheaf conjecturally has information as much as Floer theory of the Lagrangian. On the other hand, exact WKB analysis is an analysis of differential equations containing the Planck constant hbar.
In this talk, I will explain how to construct a sheaf quantization over the Novikov ring of the spectral curve of an hbar-differential equation, by using the ideas of exact WKB analysis and spectral network. In the construction, one can see how (conjecturally) the convergence in WKB analysis are related to the convergence of Fukaya category. In degree 2, the sheaf quantization associates a cluster coordinate which is the same as Fock—Goncharov coordinate. I will also mention about some relationships to Riemann—Hilbert correspondence of D’Agnolo—Kashiwara and Kontsevich—Soibelman.
https://msu.zoom.us/j/95159415920?pwd=bUlETkdpazdiWGNjZnNkUWNIaXRFQT09