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                * Princeton Discrete Math Seminar *
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Date: Thursday 27th September, 2.00 in Fine Hall 224
 
Speaker: Wesley Pegden (NYU)

Title: Apollonian structure in the Abelian sandpile

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.  
Though the sandpile has been the object of study from a diverse set of 
perspectives, even some of the most basic questions about the terminal 
configurations produced by the process have remained 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 mathematical explanation for the fractal 
nature of the sandpile which comes from a peculiar conjecture connecting 
Apollonian circle packings to integer superharmonic functions on the 
lattice.    Time permitting, we will discuss the path to a proof of the 
conjecture.  (Joint work with Charles Smart and Lionel Levine.)


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Next week: Sanjeev Arora

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