I am a Professor at the Santa Fe Institute. I work on problems at the interface of physics, computer science, and mathematics, such as phase transitions in statistical inference. When the amount of noise in a data set crosses a critical threshold, it can suddenly become impossible to find underlying patterns in it, or even tell if a pattern is really there. This includes finding communities in social and biological networks, or clusters in high-dimensional data, or structure in noisy matrices and tensors. How can we locate these phase transitions, and what informational and computational barriers do they create?
I have also worked on phase transitions in search and optimization problems, where problems suddenly become unsolvable when they become too constrained; quantum computation and quantum algorithms for the Graph Isomorphism problem; the computational complexity of predicting physical systems, and of solving systems of equations; percolation, topological defects, and Monte Carlo algorithms; games, tilings, and cellular automata; the stability of financial markets, epidemics in networks, and universality in human language; the combinatorics of proof-of-stake blockchains; and braided orbits in the three-body problem.
In addition to my technical work, I have started working on fairness and justice in algorithms, especially on issues of transparency and contestability. With colleagues at UNM in Law, Computer Science, and Political Science, as well as colleagues at SFI, I am part of the Interdisciplinary Working Group on Algorithmic Justice. We recently submitted a comment on proposed changes to Housing and Urban Development regulations that would allow discrimination lawsuits to be deflected by algorithms for lending and risk assessment of buyers and tenants, without adequate transparency or auditing for fairness.
Here is a piece on uncertainty, platonism, and pluralism in mathematics, with some observations about society with John Kaag, reprinted from The American Scholar.
Finally, like many scientists I am doing my best to understand the COVID-19 pandemic. Here is a short piece on the fact that the reproductive number R0 is only an average: it's important to take into account how it varies between regions and groups, and note that even if R0 is below 1 there is a heavy tail of surprisingly large outbreaks, especially when superspreading events take place.
Here are two animated applets by UNM undergraduate Rory McGuire: Union-find (with path compression), and 2-3-4 Trees.
I used to want Martin Gardner's old job, but I think Vi Hart would be even better at it.
One of the highest professional honors I have received.
For many years, I was blessed with a cat named Spootie.
I am a big fan of Vladimir Nabokov. Here are some of his favorite words.
Here are definitions of words from the Alchymist's Journal by Evan S. Connell (recommended to me by the inimitable Cosma Shalizi).
Here are a few poems by my grandfather, Louis Untermeyer.
I have been known to cite fictional books.
I and Mats Nordahl are the editors-in-chief of the Journal of Unpublished Results, and I also edit the Journal of Weird-Ass Shit.
Finally, here is a list of restaurant reviews for Santa Fe and Paris. Of course, these are my own personal opinions, which, though correct, may or may not be shared by my employers. They are also often sadly out of date.