Self assembly is the idea of creating a system whose component parts spontaneously assemble into a structure of interest. In this talk I will outline our research program aimed at creating self-assembled structures out of very small spheres, that bind to each other on sticking. The talk will focus on

(i) some fundamental mathematical questions in finite sphere packings (e.g. how do the number of rigid packings grow with N, the number of spheres);

(ii) algorithms for self assembly (e.g. suppose the spheres are not identical, so that every sphere does not stick to every other; how to design the system to promote particular structures);

(iii) physical questions (e.g. what is the probability that a given packing with N particles forms for a system of colloidal nanospheres); and

(iv) comparisons with experiments on colloidal nanospheres.