Random packings and liquid crystals

Abstract: Let T be a subset of R^d, such as a ball, a cube or a cylinder, and consider all possibilities for packing translates of T, perhaps with its rotations, in some bounded domain in R^d. How does a typical packing of this sort look like? One mathematical formalization of this question is to fix the density of the packing and sample uniformly among all possible packings with this density. The question arises naturally in the sciences, where T may be thought of as a molecule and its packing is related to the spatial arrangement of molecules of a material under given conditions. In some cases, the material forms a liquid crystal - states of matter which are, in a sense, between liquids and crystals. I will review ideas from this field, mentioning some of the predictions and the mathematical progress. The talk is meant to be accessible to a general mathematical audience.

Youtube link to the recording