On the Strong Density Conjecture for Apollonian Circle Packings

Name: On the Strong Density Conjecture for Apollonian Circle Packings
Uploaded: 2019-05-03T07:00:05.000Z
Duration: 1 h 4 min 37 s
Channel: Alex Kontorovich
Description: Alex Kontorovich presents joint work with Jean Bourgain on the Strong Density Conjecture for Apollonian circle packings, demonstrating that a set of density one…

Alex Kontorovich

Rutgers University·Alex Kontorovich

1:04:37

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On the Strong Density Conjecture for Apollonian Circle Packings

Alex Kontorovich Rutgers University

1:04:37·2019·research·Research Seminar

Alex Kontorovich presents joint work with Jean Bourgain on the Strong Density Conjecture for Apollonian circle packings, demonstrating that a set of density one satisfies the conjecture with a power savings on the exceptional set. The talk delves into the interplay between number theory, geometry, and the properties of thin groups.

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.

Mathematics Philosophy Number Theory & Abstract Algebra Geometry Apollonian Circle Packings Density Conjectures Thin Groups

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Alex Kontorovich

Professor of Mathematics

Alex Kontorovich is a Professor of Mathematics at Rutgers University, renowned for his research in analytic number theory, especially on Apollonian circle packings.

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