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Alex Kontorovich - On the Strong Density Conjecture for Apollonian Circle Packings [2012]

slides for this talk: https://docs.google.com/viewer?url=ht... Abstract: The Strong Density Conjecture states that for a given primitive integral Apollonian circle packing, every sufficiently large admissible (passing local obstructions) integer is the curvature of some circle in the packing. In joint work with Jean Bourgain, we prove that a set of density one satisfies the conjecture, with a power savings on the exceptional set. On the Strong Density Conjecture for Apollonian Circle Packings Hot Topics: Thin Groups And Super-Strong Approximation February 06, 2012 - February 10, 2012 February 06, 2012 (03:40 PM PST - 04:40 PM PST) Speaker(s): Alex Kontorovich (Rutgers University) Location: MSRI: Simons Auditorium http://www.msri.org/workshops/652/sch...