School of Mathematical Sciences

Department Colloquium

Schreiber 006, 12:15

Cornell University

Let n particles starting at the origin in Z^2 spread out by a

Abstract:

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