Lionel Levine

Professor
Department of Mathematics
Cornell University

AI Safety  |  Math  |  Papers  |  Talks  |  Teaching  |  Gallery  |  Fun!  |  Contact  |  CV

AI Safety

I'm a mathematician working on AI safety. My research is aimed at increasing the probability that future AI systems benefit all of humanity and the planet. Some things I've worked on are how to quantify value alignment and character traits in language models, a definition of AGI, a mathematical reasoning benchmark, a metric for belief coherence, and hidden incentives for planning.

I'm a faculty advisor for Cornell AI Alignment and the Cornell Math+AI Lab, and I teach a graduate course on Math for AI Safety.

I thank Open Philanthropy / Coefficient Giving for supporting my transition into AI safety during 2023–2025. I'm seeking funding to continue this important work. If your organization funds AI safety research, I'd love to connect!

Math

In my past life as a pure mathematician I studied 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.


Some highlights of my pure math 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.

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.

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

Papers and preprints (my papers on arXiv):

Selected talks:

Teaching:

Expository notes:

Some unpublished papers and notes: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!

Contact:

Thanks for visiting my homepage! You can find me at @lionellevine or lionel.levine@cornell.edu