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Analysis Seminar

Friday, December 13, 2019
3:00pm to 4:00pm
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Linde Hall 255
Conformal Welding of Dendrites
Peter Lin, Department of Mathematics, Stony Brook University,

If K is a connected, locally connected, compact subset of the plane, then a Riemann map f: C-D \to C-K extends continuously to the unit circle. Thus K induces an equivalence relation on the circle $x\sim y iff f(x)=f(y)$.

One can ask the converse question: given an equivalence relation on the circle, is there a conformal map realizing this equivalence?

This is essentially the conformal welding problem. In this talk we discuss some criteria for the existence for such a map. We give example applications of this criteria for equivalence relations arising in dynamics and probability. Joint with Steffen Rohde.

For more information, please contact Math Department by phone at 626-395-4335 or by email at mathinfo@caltech.edu.