Tel-Aviv University
School of Mathematical Sciences

Department Colloquium

Monday, December 17, 2012

Schreiber 006, 12:15

Lionel Levine

Cornell University

Scaling Limit of the Abelian Sandpile

Let n particles starting at the origin in Z^2 spread out by a
deterministic rule: At each time step, each site with 4 or more
particles sends one particle to each of its neighbors (North, South,
East and West). The resulting final configuration has a complex
fractal structure that remains mysterious.  In a breakthrough work in
2011, Pegden and Smart proved existence of its scaling limit as n goes
to infinity.  Their insight was to ask which functions on R^2 can be
expressed as limits of superharmonic functions from (1/n) Z^2 to
(1/n^2) Z.  I will discuss joint work with Pegden and Smart on the
case of quadratic functions, where this question has a surprising and
beautiful answer: the maximal such quadratics are classified by the
circles in a certain Appolonian circle packing of R^2.

Coffee will be served at 12:00 before the lecture
at Schreiber building 006