|Date: Friday, October 10, 2014
Location: 1084 East Hall (3:00 PM to 4:00 PM)
Title: Topological Similarity of Random Cell Complexes, and Applications
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 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). This approach also allows a distance to be defined that measures the similarity of the local topology of two cell complexes. The distance is used to identify a steady state of a model dislocation network evolving by energy minimization, and then to quantify the approach of the simulation to this steady state.
If time permits, I will introduce two other methods of computational topology useful to the study of materials.
Speaker: Benjamin Schweinhart
Institution: Princeton University