Numerics of Riemann-Hilbert problems and operator determinants (B03)

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The numerical treatment of Riemann-Hilbert problems, e.g., from the isomonodromy transform of discrete holomorphic functions, requires the study of the interplay of asymptotic (continuous) and pre-asymptotic (discrete) structures. Preconditioning based on contour deformations, lensing and g-functions leads to the computation of shortest pathes in families of weighted graphs subject to some homotopy constraints. Integrable kernels lead to equivalent formulations in terms of operator determinants. Numerical methods require smooth kernels that can be obtained from discrete symmetries. The basic concept of Hilbert transforms will be studied within the framework of discrete complex analysis.