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Masterclass: Riemann–Hilbert problems

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CATW03 - Computational complex analysis

Riemann–Hilbert problems are complex analytical problems where a jump is specified on a complicated contour, often with multiple self-intersections and open endpoints. The numerical methods for singular integrals in Part I lead naturally to an effective collocation scheme provided extra care is taken at self-intersections to ensure the solution is sectionally analytic and smoothness is preserved. Applications discussed include special functions, integrable PDEs, computing orthogonal polynomials, and computing random matrix statistics.

We will demonstrate these results in Julia using RiemannHilbert.jl.

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

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