Circle Packings and Elliptic Curves

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• Edward Crane, Bristol
• Tuesday 11 March 2008, 16:00-17:00
• 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 2-sphere, 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 P-functions.

This talk is part of the Discrete Analysis Seminar series.

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