UBC Math Department Colloquium: Miranda Holmes Cerfon

Particles on the scale of nanometres to micrometres may be used as building blocks for new materials, with a variety of applications e.g. in optics, drug delivery, energy harvesting, and nanorobotics. A goal for theory and simulation is to build algorithms to find the building blocks that assemble into a structure of interest. This is a challenge because structures that are designed to be the most thermodynamically stable, are often kinetically inaccessible — they take an infeasible amount of time to assemble. We address this challenge in two ways, First, we take inspiration from biology, and observe that many complex biological systems assemble hierarchically — they first build subunits, that later assemble into larger entities, in a process that can repeat over several generations. I will show how we can emulate this process in particle systems to create objects with high yield that assemble hierarchically and spontaneously over at least five generations. Next, we ask how we can do even better, by directly optimizing the interactions for small systems. Doing so led us to an unexpected connection to the combinatorial properties of graphs, which informs strategies for designing kinetically optimal interactions in much larger systems.