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Computing all zeros of harmonic mappings in the plane

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CATW01 - The complex analysis toolbox: new techniques and perspectives

We present a continuation method to compute all zeros of certain harmonic mappings $f$ in the complex plane. While tracing the homotopy curves of $f$ is done by a prediction correction approach, the main difficulty is to handle the bifurcations and turning points. To achieve this we study the critical curves and caustics of $f$. Moreover, we illustrate our method with several examples and discuss possible extensions.

This is joint work with Olivier Sète (TU Berlin).

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

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