Benjamin Schweinhart

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  Topological Similarity of Cell Complexes
  Benjamin Schweinhart
  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.