Title : Conformal welding homeomorphisms.
Abstract : Conformal welding is a correspondence between circle homeomorphisms and curves in the plane. It has appeared over the years to be of considerable interest in several areas of mathematics and applications, such as Teichmüller Theory, Kleinian Groups, computer vision and pattern recognition, and so forth.
The uniqueness of conformal welding has been known for a long time to be closely related to the notion of conformal removability. In fact, many papers in the literature claim, using the same argument, that uniqueness is characterized precisely by the removability of the curve. In this talk, I will show that this argument is actually incorrect, so that the problem of characterizing uniqueness of conformal welding remains open.