Lionel Levine

Associate Professor
Department of Mathematics
Cornell University

Email: my last name at
Office: 438 Malott Hall

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See WHAT IS a sandpile? for a non-technical overview.

I study abelian networks, an invention of the statistical physicist Deepak Dhar, who called them "abelian distributed processors." In one point of view, abelian networks are discrete dynamical systems with a certain strong convergence property. From another point of view, they are a means of associating algebraic invariants to graphs. In yet a third viewpoint, they are a model of asynchronous computation: nodes of the network pass messages along edges to perform a computation requiring no central control over timing.

Some other things I've worked on since my Ph.D. are the scaling limit of the abelian sandpile in Z^2 where an Apollonian circle packing makes a surprise appearance, the devil's staircase for parallel chip-firing, refuting the density conjecture for sandpiles, logarithmic fluctuations for internal DLA, fast simulation of growth models, a generalization of Knuth's formula for spanning trees, and word equations in uniquely divisible groups.

My Ph.D. thesis, advised by Yuval Peres at Berkeley, used ideas from free boundary problems in PDE to prove limiting shape theorems for growth models in probability and combinatorics.

I thank the National Science Foundation and the Sloan Foundation for supporting my research.

Papers and preprints:

Expository notes:

Selected talks:


Some unpublished papers and notes:

Odds and Ends: