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Junior Geometry
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William Winston, PMA 12.166: Quasiconformal Maps and the MRMT
Tuesday, April 04, 2023, 03:45pm - 04:45pm
Quasiconformal (qc) maps are generalizations of conformal maps in the following sense: infinitesimal circles are mapped to infinitesimal ellipses in a bounded way. After a review on conformal maps, we start the talk by making sense of this. Through this notion, one can formulate the so-called measurable Riemann mapping theorem (MRMT), a helpful tool in surface topology, for instance. We'll discuss some heuristics to prove the MRMT. Finally, we will close with some applications of qc maps in geometry/topology. In spite of the MRMT, no background in measure theory or PDE will be assumed.
Location: PMA 12.166

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