__Computing Operator Determinants and Preconditioning Riemann-Hilbert Problems - A Numerical Analyst's Encounter with Mathematical Physics__

F. Bornemann

**Abstract**

The numerical evaluation of operator determinants, originally born out of an attempt to validate some highly structured differential equations calculations, has become a popular tool in areas of Mathematical and Theoretical Physics dealing with integrable systems; e.g., it was recently used by S. Nishigaki to calculate the 'pion decay constant' of certain QCD-like theories. We review some of this development, tell an amusing story about the numerical evaluation of higher-order derivatives and its relation to a problem in graph theory, and end by showing how all this generalizes to the preconditioning of matrix-valued Riemann-Hilbert problems.
Partly joint work with my PhD student Georg Wechslberger (TU München).