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SUMMARY:An Asymptotic Local-Global Principle for Integral Kleinian Sphere 
 Packings - Edna Jones (Rutgers University)
DTSTART:20210309T143000Z
DTEND:20210309T153000Z
UID:TALK156553@talks.cam.ac.uk
DESCRIPTION:We will discuss an asymptotic local-global principle for\ncert
 ain integral Kleinian sphere packings. Examples of Kleinian sphere\npackin
 gs include Apollonian circle packings and Soddy sphere packings.\nSometime
 s each sphere in a Kleinian sphere packing has a bend\n(1/radius) that is 
 an integer. When all the bends are integral\, which\nintegers appear as be
 nds? For certain Kleinian sphere packings\, we\nexpect that every sufficie
 ntly large integer locally represented\neverywhere as a bend of the packin
 g is a bend of the packing. We will\ndiscuss ongoing work towards proving 
 this for certain Kleinian sphere\npackings. This work uses the circle meth
 od\, quadratic forms\, and\nspectral theory.
LOCATION:Online
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