Computer-assisted proofs for finding the monodromy of hypergeometric differential equations

Abstract: In this talk, we introduce a numerical method for rigorously finding the monodromy matrix of hypergeometric differential equations. From a base point defined by fundamental solutions, we analytically continue the solution on a contour around a singular point of the differential equation using a rigorous integrator. Depending on the contour we obtain the monodromy representation of fundamental solutions, which represents the fundamental group of the equation. As an application of this method, we consider a Picard-Fuchs type hypergeometric differential equation arising from a polarized K3 surface. The monodromy matrix shows a deformation of homologically independent 2-cycles for the surface along the contour, which is regarded as a change of characterization for the K3 surface. This is joint work with Naoya Inoue (University of Tsukuba) and Toshimasa Ishige (Chiba University).

analysis of PDEsclassical analysis and ODEsdynamical systemsfunctional analysisnumerical analysis

Audience: researchers in the discipline

CRM CAMP (Computer-Assisted Mathematical Proofs) in Nonlinear Analysis

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