Circle Packings and Elliptic Curves
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 Edward Crane, Bristol
 Tuesday 11 March 2008, 16:0017:00
 MR13, CMS.
If you have a question about this talk, please contact Ben Green.
The topic of circle packings dates back to a theorem of Koebe from the
1930s, saying that any triangulation of the sphere can be represented
by a finite collection of geometric discs in the standard 2sphere,
one for each vertex, such that adjacent vertices correspond to
externally tangent discs. Moreover the resulting circle packing is
unique up to Mobius transformations. The theorem was rediscovered in
different contexts firstly by Andreev and then by Thurston, who
reinterpreted it as a discretization of the conformal structure on the
Riemann sphere and gave an algorithm for computing the packing.
Thurston’s ideas have been developed into an interesting theory of
“discrete analytic functions”. I will describe the highlights of this
theory, outline some open problems, and then show how to construct
discrete versions of Weierstrass Pfunctions.
This talk is part of the Discrete Analysis Seminar series.
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