Philadelphia Area Number Theory Seminar

Wednesday, March 4, 2020 - 2:15pm

Holley Friedlander

Dickinson College

An Apollonian circle packing is a fractal arrangement of circles with disjoint interiors formed starting from four mutually tangent circles and continually adding newer circles in the triangular interstices of any subset of three. If four mutually tangent circles in the packing have integer curvature, then all circles in the packing will have integer curvature. Given such a packing, there are natural questions one can ask. For example, it is conjec-tured that, subject to a congruence obstruction, the collection of curvatures contains every suÿciently large admissible integer. In this talk, we investigate the arithmetic properties of the collection of integers appearing in prime components of Apollonian circle packings.