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
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).