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CATEGORIES:Discrete Analysis Seminar
SUMMARY:Circle Packings and Elliptic Curves - Edward Crane
\, Bristol
DTSTART;TZID=Europe/London:20080311T160000
DTEND;TZID=Europe/London:20080311T170000
UID:TALK9065AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/9065
DESCRIPTION:The topic of circle packings dates back to a theor
em of Koebe from the\n1930s\, saying that any tria
ngulation of the sphere can be represented\nby a f
inite collection of geometric discs in the standar
d 2-sphere\,\none for each vertex\, such that adja
cent vertices correspond to\nexternally tangent di
scs. Moreover the resulting circle packing is\nuni
que up to Mobius transformations. The theorem was
rediscovered in\ndifferent contexts firstly by And
reev and then by Thurston\, who\nreinterpreted it
as a discretization of the conformal structure on
the\nRiemann sphere and gave an algorithm for comp
uting the packing.\nThurston's ideas have been dev
eloped into an interesting theory of\n"discrete an
alytic functions". I will describe the highlights
of this\ntheory\, outline some open problems\, and
then show how to construct\ndiscrete versions of
Weierstrass P-functions.
LOCATION:MR13\, CMS
CONTACT:Ben Green
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