**Lionel Levine**

**Monday, March 24, 2014**

4:00pm 310 Gates Hall

**Abstract:**
A sandpile on a graph is an integer-valued function on the vertices.
It evolves according to local moves called "topplings". Some sandpiles
stabilize after a finite number of topplings, while others topple
forever. For any sandpile s_0 if we repeatedly add a grain of sand at
an independent random vertex, we eventually reach a sandpile s_\tau
that topples forever. Statistical physicists Poghosyan, Poghosyan,
Priezzhev and Ruelle conjectured a precise value for the expected
amount of sand in this "threshold state" s_\tau in the limit as s_0
goes to negative infinity. I will outline the proof of this conjecture
in http://arxiv.org/abs/1402.3283 and mention some algorithmic open
questions.