#### Abstract

Although random cell complexes occur throughout the physical sciences, there does

not appear to be a standard way to quantify their statistical similarities and differences. I'll

introduce the method of swatches, which describes the local topology of a cell complex in terms

of probability distributions of local configurations. It allows a distance to be defined which

measures the similarity of the local topology of cell complexes. Convergence in this distance is

related to the notion of a Benjamini Schramm graph limit. In my talk, I will use this to state

universality conjectures about the long-term behavior of graphs evolving under curvature flow,

and to test these conjectures computationally. This system is of both mathematical and physical

interest.

If time permits, I will discuss other applications of computationally topology to curvature flow

on graphs, and describe recent work on a new notion of geometric graph limit.