Masterclass: oscillatory Riemann-Hilbert problems – Sheehan Olver (Imperial College London); Thomas Trogdon (University of Washington)

December 13, 2019 @ 9:00 am – 10:00 am
Seminar Room 1
Newton Institute

Riemann-Hilbert problems arising in applications are often oscillatory presenting challenges to their numerical solution. An effective scheme for determining their asymptotic behaviour is Deift-Zhou steepest descent, which mirrors steepest descent for oscillatory integrals by deforming to paths that turn oscillations to exponential decay. This is a fundamental result that lead to numerous important rigorous asymptotic results over the last 35+ years. This technique proves useful for numerics as well providing a convergent approach that is accurate both in the asymptotic and non-asymptotic regime. Recent progress on going beyond steepest descent and solving oscillatory problems without deformation using GMRES is also discussed.