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.
Here is a preprint on the behavior of epidemics in networks with directed transmission, i.e., where the disease is more likely to flow from one person to another than the reverse: for instance, if one is wearing a mask and the other isn't. We distinguish two kinds of individuals: those with high risk (of being infected by many others) and those with high spread (who might pass it on to many others). This creates a forward and backward version of the classic "friendship paradox", and suggests that backwards contact tracing could be an important strategy in controlling the epidemic.
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.