How does nature make us? The central structure of biology has astonishing mathematical precision: life on earth is transmitted through a genetic code and this genetic code evolves in a grand game of chance called evolution. Yet biology is the least understood, in mathematical terms, of the three fundamental branches of the sciences -- biological, chemical and physical. Further, the central aesthetic of mathematics the idea of unity, is very different from the proliferation of minutiea that seems to characterize life in all its glorious messiness.

I never fail to be inspired by Woese's painstaking organization of the taxonomy of life based on the biochemistry of archaea and the modern challenge of classifying the tree of life. But a challenge of being a `grown-up' mathematician, is that one feels compelled to choose between structured problems, with familiar mathematics, and the practical challenges of being a specialist in an area of biology. The study of self-assembly offers a median path -- the study of microscale experimental systems that capture part of the mysterious interplay between coding, geometry and biochemical function -- while still offering genuine mathematical insight.

Our main contributions in the area are the design of model experimental systems, and the discovery of simple design rules that collapse large spaces of possible assembly states, into simple hubs that provide reliable self-assembly. I am particularly proud of our comprehensive paper in Artificial Life. I'm not sure if anyone will ever read it, since its not in the flashiest journal. But it has a cool name, and its a good paper, so if you're going to pick from this list, that's the one.

Papers on self-assembly

The building game: from enumerative combinatorics to conformational diffusion. With Daniel Johnson-Chyzhykov. Journal of Nonlinear Science, Vol. 26 (2016).

Energy landscapes for the self-assembly of supramolecular polyhedra . with Emily Russell. Journal of Nonlinear Science, Vol. 26 (2016) .

Self-assembly of mesoscale isomers: the role of pathways and degrees of freedom. With David Gracias, Daniel Johnson, Ryan Kaplan, Joe Klobusicky and Shivendra Pandey. PLoS One (Oct. 2014).

Building polyhedra by self-assembly: theory and experiment . With David Gracias , Ryan Kaplan, Joe Klobusicky and Shivendra Pandey. Artificial Life (Vol.20, Issue 4, Fall 2014).

Algorithmic design of self-folding polyhedra. With Shivendra Pandey, Maggie Ewing, Drew Kunas, Nghi Nguyen and David Gracias. PNAS ( Oct. 28, 2011).

The Sphereprint: An approach to quantifying the conformability of flexible materials. With Andrew Sageman-Furnas, Parikshit Goswami and Stephen Russell, Journal of Textile Research (2013).
This paper is not really on self-assembly, but its on soft matter and experimental techniques, which is why it's here.

Video links

Talk at Kavli Frontiers of Science, 2012

NSF Science Nation coverage of our work (2012)