Special Colloquium
Wesley Pegden
NYU
Apollonian structure in the Abelian sandpile
Abstract: The Abelian sandpile is a chip-firing game on the lattice which can be viewed as a simple deterministic analog
to stochastic diffusion processes based on random walks. In contrast to its stochastic counterparts,
the sandpile produces striking fractal scaling limits which have long resisted explanation, or even precise
description. In this talk, we will discuss a new approach to understanding the fractal behavior of the
sandpile, which begins by identifying sandpile limits as solutions of a certain PDE. The heart of our
results is a surprising connection between the integer superharmonic functions on the lattice which
govern this PDE and Apollonian circle packings of the plane, which allows a characterization of certain
fractal solutions produced by the sandpile.
Tea at 4
Wednesday December 5, 2012 at 3:00 PM in SEO 636