Cluster coordinates from sheaf quantization of spectral curve

Abstract: A sheaf quantization is a sheaf associated to a Lagrangian brane. In this talk, I will explain my construction of sheaf quantization of the spectral curves of Schrodinger equations, which is a part of conjectural $\hbar$-Riemann—Hilbert correspondence. The construction is based on exact WKB analysis. I will also explain an application to cluster theory. Iwaki—Nakanishi have found cluster variables in exact WKB analysis. The construction of sheaf quantization gives a geometric explanation of Iwaki—Nakanishi’s cluster variables and their variants. A part of this talk is based on my joint work in progress with T. Ishibashi.

algebraic geometrycombinatoricsdifferential geometrygeometric topologyquantum algebrarepresentation theorysymplectic geometry

Audience: researchers in the topic

Legendrians, Cluster algebras, and Mirror symmetry

Series comments: Schedule
School: January 4–8, 2021
Conference: January 11–15, 2021