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SUMMARY:Circle Packings and Elliptic Curves - Edward Crane\, Bristol
DTSTART:20080311T160000Z
DTEND:20080311T170000Z
UID:TALK9065@talks.cam.ac.uk
CONTACT:Ben Green
DESCRIPTION:The topic of circle packings dates back to a theorem of Koebe 
 from the\n1930s\, saying that any triangulation of the sphere can be repre
 sented\nby a finite collection of geometric discs in the standard 2-sphere
 \,\none for each vertex\, such that adjacent vertices correspond to\nexter
 nally tangent discs. Moreover the resulting circle packing is\nunique up t
 o Mobius transformations. The theorem was rediscovered in\ndifferent conte
 xts firstly by Andreev and then by Thurston\, who\nreinterpreted it as a d
 iscretization of the conformal structure on the\nRiemann sphere and gave a
 n algorithm for computing the packing.\nThurston's ideas have been develop
 ed into an interesting theory of\n"discrete analytic functions". I will de
 scribe the highlights of this\ntheory\, outline some open problems\, and t
 hen show how to construct\ndiscrete versions of Weierstrass P-functions.
LOCATION:MR13\, CMS
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