# Jerusalem Mathematics Colloquium

Thursday, 4th December 2008, 4:00 pm

Mathematics Building, Lecture Hall 2

##

Klaus Schmidt

(University of Vienna)

"Sandpiles and the Harmonic Model"

** Abstract: **

The *d*-dimensional abelian sandpile model is a lattice model
introduced in 1987 by Bak, Tang and Wiesenfeld as an example of
what they called `self-organized criticality'. Although this
deceptively simple model has been studied quite intensively
both in the physics and mathematics literature, some very basic
questions about it are still open, like its properties under two
different kinds of dynamics: `addition' (of
grains of sand), and the shift-action.
By extending an algebraic construction originally introduced by
A. Vershik for Markov partitions of hyperbolic automorphisms of the
2-torus one can show that the sandpile model is closely related to a
certain *Z^d*-action by automorphisms of a compact
abelian group, the `harmonic model'.

The purpose of this lecture (which is based on joint work with
Evgeny Verbitskiy) is a discussion of this construction and of the
conclusions that can be drawn from the connection between these systems.

Light refreshments will be served in the faculty lounge at 3:30.

List of talks, 2008-09

Archive of talks