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You are here: Homepage » Seminars - Academic year 2022-23 » Combinatorics Seminar » Michael Dobbins (Binghamton)

seminars:comb:abstract.201909dob

A map is called conformal when it preserves angles. Consider a sequence of simple closed curves C_{t} in the plane that get squished to a path. That is, C_{t} consists of a pair of curves E_{t} and W_{t} that converge to the same curve in Fréchet distance. By the Riemann Mapping Theorem, there is a conformal map from the interior of C_{t} to the upper half-plane. Preserving angles comes at the cost of distorting scale, and as C_{t} gets squished, this map becomes highly distorted. I will show in this talk that, for appropriate choice of conformal map, the image of any arbitrarily small neighborhood of a single point covers the entire upper half-plane in the limit.

seminars/comb/abstract.201909dob.txt · Last modified: 2020/01/29 14:03 (external edit)

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