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Masterclass: oscillatory Riemann-Hilbert problems

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CATW03 - Computational complex analysis

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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Riley Auditorium, Clare College Memorial Court, Queen's Road Centre for Mathematical Sciences, Wilberforce Road, Lecture room MR14 (Pavilion F) Darwin College Lecture Series

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