My research is in topological combinatorics and stochastic topology. My work has primarily focused on homological statistics and collapsibility phase transitions in random simplicial complexes. Recently I have become more interested in the applications of random topology to data analysis, where the aim is to use topological methods and constructions to study the underlying "shape" of potentially high-dimensional data sets. On the flip side of these probabilistic questions, I also study extremal topology and geometry in polygonal and polyhedral cell complexes. And from my early background in graph theory, I maintain a deep affection for the topic of graph colorings and homomorphisms.