Description
Department Colloquium.
Speaker: Lionel Levine, Cornell University.
Time: Wednesday, 06 February, 4pm.
Venue: Ramanujan Hall.
Title: Circles in the sand.
Abstract: I will describe the role played by an Apollonian circle packing
in the scaling limit of the abelian sandpile on the square grid Z^2. The
sandpile solves a certain integer optimization problem. Associated to each
circle in the packing is a locally optimal solution to that problem. Each
locally optimal solution can be described by an infinite periodic pattern
of sand, and the patterns associated to any four mutually tangent circles
obey an analogue of the Descartes Circle Theorem. Joint work with Wesley
Pegden and Charles Smart.