### Rutgers Discrete Mathematics Seminar

Title: The fractal nature of the Abelian Sandpile

Speaker: **Wes Pegden**, NYU

Date: Tuesday, February 7, 2012 2:00pm

Location: Hill Center, Room 124, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:
The Abelian Sandpile is a diffusion process on
configurations of chips on the integer lattice, in which a vertex with
at least 4 chips can "topple", distributing one of its chips to each
of its 4 neighbors. This process can be shown to Abelian in the sense
that if topplings are perfomed until no more topplings are possible,
the order in which we choose to perform topplings will not affect the
final configuration. Though the Sandpile has been the object of study
from a diverse set of perspectives, many of the most basic questions
about the results of this process remain unanswered. One of the most
striking features of the sandpile is that when begun from a large
concentration of n chips, the resulting terminal configurations seem
to converge to a peculiar fractal pattern as n goes to infinity. In
this talk, we will discuss a new mathematical explanation for the
fractal nature of the sandpile. (Joint work with Charles Smart and
Lionel Levine).

See: http://math.rutgers.edu/seminars/allseminars.php?sem_name=Discrete%20Math