Conformal welding: A tale of curves and homeomorphisms
Conformal welding is a correspondence between Jordan curves in the plane and circle homeomorphisms. It seems to have first been considered in 1936 by Courant, in his solution of the Plateau-Douglas problem of minimal surfaces. Since then it has proven to be a fundamental tool in complex analysis and related areas, such as Teichm¨uller theory, holomorphic dynamics, Kleinian groups and more recently, numerical pattern recognition and random conformal geometry. The first part of this talk will consist of a survey of conformal 7welding, including its main properties and some open problems. In the second part of the talk I will present a new application of conformal welding to a certain matching problem for analytic functions introduced by Ebenfelt, Khavinson and Shapiro. As we will see this is closely related to the question of which subsets of the Riemann sphere are rational lemniscates. This is based on joint work with Kirill Lazebnik and Pierre-Olivier Parisé.
Event Timeslots (1)
Tuesday
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