Abstracts
for the Seminar
Discrete Geometry and
Combinatorics
Spring 2012
Speaker: R. Connelly
Title: Periodic Planar Disk Packings
Time: 2:30 PM,
Monday, February 6, 2012
Place: Malott 206
Abstract:
Several
conditions are given when a packing of equal disks in a torus is
locally maximally dense, where the torus is defined as the quotient of
the plane by a two-dimensional lattice. Conjectures are presented that
claim that the density of any strictly jammed packings, whose
graph does not consist of all triangles and the torus lattice is the
standard triangular lattice, is at most
$\frac{n}{n+1}\frac{\pi}{\sqrt{12}}$, where $n$ is the number of
packing disks. Several classes of collectively jammed packings
are presented where the conjecture holds.