## Topological similarity of random cell complexes, and applications

Benjamin Schweinhart

Princeton University

December 10, 2014

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 notions of a 'swatch' and a 'cloth', which provide a description of the local topology of cell complexes which is both general (any physical system that may be represented as a regular cell complex is admissible) and complete (any statistical question about the local topology may be answered from the cloth).