主 题: Apolorian Circle Packings:Combinatorics Geometry, and Group Theory
报告人: Prof. Catherine Yan (Texas A & M University)
时 间: 2006-06-09 下午 2:30 - 3:30
地 点: 理科一号楼 1114(数学所活动)
Apollonian circle packings arise by repeatedly filling the interstices
between mutually tangent circles with further tangent circles.
It is possible for every circle in such a packing to have
integer radius of curvature. In fact, it is even possible for
a packing to be oriented in the Euclidean plane so that for
each circle $C_i$ in the packing with center $(x_i,y_i)$ and radius of
curvature $r_i$, all the quantities $r_i$, $r_i x_i$ and $r_i y_i$
are integers.
In this talk we study these remarkable packings from combinatorial,
geometric, and group theoretical approaches. We establish a
generalization of the Descartes equations which characterizes
Apollonian circle packings, describe two group actions on the family
of packings, and investigate the integrality properties in terms
of the curvatures and centers of the circles. Time permits, we will
also touch on higher-dimensional analogs of these packings.
