Explore statistical topology of random cell complexes and their applications in this 59-minute lecture by Benjamin Schweinhart. Delve into topics such as curvature flow on graphs, grain growth, and embedded graphs. Learn about existence and uniqueness in computational results, graph representation, and the tree of swatches. Examine swatch types, distances on swatches and cell complexes, and gain insights into Benjamin Schramm graph limits. Investigate the steady state hypothesis and its computational evidence. This comprehensive presentation, organized by the Applied Algebraic Topology Network, offers a deep dive into the intersection of statistical topology and random structures, providing valuable knowledge for researchers and students in the field.