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SPEAKER: Dimitrios Ntalampekos (Stony Brook University)

HOST: Vyron Vellis

TITLE: Removability of fractal sets and related problems

ABSTRACT: The problem of removability of a set, in general, asks whether one can glue functions of a given class along that set and obtain a function lying in the same class. In particular, removability of sets for the class of conformal maps has applications in Complex Dynamics, in Conformal Welding, and in other problems that require gluing of functions. We, therefore, seek geometric conditions on sets that guarantee their removability. In this talk, I describe my work on the (non)removability of fractal sets with infinitely many complementary components, such as the Sierpinski gasket and Sierpinski carpets. Moreover, I will discuss work with Younsi towards a conjecture that relates removability to another problem of Geometric Function Theory, namely the rigidity of circle domains. One of the main techniques in my results involves the construction of an abstract metric surface homeomorphic to the Euclidean plane and the embedding of that surface back to the plane with controlled distortion.

Friday, October 30 at 3:35pm to 4:35pm

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