ℏ-Riemann-Hilbert correspondence

2022/02/09 by Tatsuki Kuwagaki, Kuwagaki, Tatsuki
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2202.04400

openalex publication_date 2022/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We formulate and prove a Riemann-Hilbert correspondence between ℏ-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.

Related

• Deformation quantization and perverse sheaves
• Sheaf quantization from exact WKB analysis
• An introduction to sheaf quantization
• Sheaf quantization in Weinstein symplectic manifolds
• On the irregular Riemann-Hilbert correspondence