The fractal nature of the Abelian Sandpile
Date
Wednesday, March 21, 2018 14:00 - 15:00
Speaker
Wesley Pegden (Carnegie Mellon U)
Location
Mondi Seminar Room 2, Central Building
Series
Seminar/Talk
Tags
Mathematics and CS Seminar, mathematical_seminar_ics
Host
Herbert Edelsbrunner
Contact
The Abelian Sandpile is a simple diffusion process on the integer lattice, in which configurations of chips disperse according to a simple rule: when a vertex has at least 4 chips, it can distribute one chip to each neighbor.Introduced in the statistical physics community in the 1980s, the Abelian sandpile exhibits striking fractal behavior which long resisted rigorous mathematical analysis (or even a plausible explanation). We now have a relatively robust mathematical understanding of this fractal nature of the sandpile, which involves surprising connections between integer superharmonic functions on the lattice, discrete tilings of the plane, and Apollonian circle packings. In this talk, we will survey our work in this area, and discuss avenues of current and future research.