Project Details
Numerics of Riemann-Hilbert problems and operator determinants (B03)
Subject Area
Mathematics
Term
from 2012 to 2020
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 195170736
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.
DFG Programme
CRC/Transregios
Subproject of
TRR 109:
Discretisation in Geometry and Dynamics
Applicant Institution
Technische Universität Berlin
Project Head
Professor Dr. Folkmar Bornemann