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SUMMARY:Ian Whitehead (Swarthmore College)
DTSTART:20210422T000000Z
DTEND:20210422T020000Z
DTSTAMP:20260423T021314Z
UID:WiSe/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WiSe/15/">Wh
 at is an Apollonian Packing?</a>\nby Ian Whitehead (Swarthmore College) as
  part of What is ...? Seminar\n\n\nAbstract\nFix four mutually tangent cir
 cles in the plane. Fill in the spaces between these circles with additiona
 l tangent circles. By repeating this process ad infinitum\, on smaller and
  smaller scales\, we obtain an Apollonian circle packing. In this talk I w
 ill sketch a proof of Descartes' theorem on circle configurations\, and in
 troduce a group which acts on packings in two different ways\, with a subt
 le duality between them. If time allows\, I will also talk about my own re
 cent work relating packings to Kac-Moody root systems. This connection is 
 via a four-variable generating function for curvatures that appear in an A
 pollonian packing\, which is essentially a character for a rank 4 indefini
 te Kac-Moody root system. I will discuss its domain of convergence\, the T
 its cone of the root system\, which inherits the rich geometry of Apolloni
 an packings.\n
LOCATION:https://researchseminars.org/talk/WiSe/15/
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