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Computing all zeros of harmonic mappings in the plane

Presented by: 
Jan Zur Technische Universität Berlin
Date: 
Tuesday 10th September 2019 - 15:00 to 15:30
Venue: 
INI Seminar Room 1
Abstract: 
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).
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons