Lionel Levine

Associate Professor
Department of Mathematics
Cornell University

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Hello, I'm Lionel! I study abelian networks. These are interacting particle systems whose final state does not depend on the order of interactions. From another point of view, they are systems of communicating automata that pass messages to perform an asynchronous computation. I was inspired to work in this area by Deepak Dhar, Cris Moore, Yuval Peres, and Jim Propp.

If you want to learn a bit about this fascinating nexus of math, computer science, and statistical physics, I recommend starting with WHAT IS a sandpile? for a non-technical overview, and Laplacian growth, sandpiles, and scaling limits for a more recent survey.

Some highlights of my research 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, asynchronous circuits with integer input and output, fast simulation of growth models, a generalization of Knuth's formula for spanning trees, and word equations in uniquely divisible groups.

I thank the National Science Foundation, Sloan Foundation, Simons Foundation, and Institute for Advanced Study for supporting my research.

I'm an editor of Combinatorial Theory, a open-source journal with no author fees and double-blind refereeing. Please submit your work to CT!

Papers and preprints (my papers on arXiv):

Expository notes:

Selected talks:


Some unpublished papers and notes:

Fun Stuff!

An integer sequence, a hat problem, a prediction contest, and how to make the most of a shared meal! Recently I've been thinking about multi-agent learning.


Thanks for visiting my homepage! You can find me at @lionellevine or (my last name) @