My research is broadly in algebraic topology. Most of it has had to do with the Goodwillie-Weiss manifold calculus of functors and its applications to embedding spaces. I have studied some ways in which this theory connects to finite type invariants and Milnor invariants. I have used both embedding and orthogonal calculus of functors to study the rational homotopy type of spaces of knots, and more generally spaces of embeddings of manifolds. I have also studied configuration space integrals and their interaction with functor calculus in the context of the topology of links, homotopy links, and braids.  In addition, I have recently started looking at r-immersions and partial configuration spaces using functor calculus techniques in hope to apply them to some problems in combinatorial topology. My most recent projects are applications of topological data analysis to UNICEF poverty data and the spread of COVID-19, as well as modeling political structures with simplicial complexes.

My book on cubical homotopy theory (published version can be purchased here), written jointly with B. Munson, covers many classical and modern topics in homotopy theory with an emphasis on cubical diagrams. The book contains over 300 examples and provides detailed explanations of many fundamental results in algebraic topology.  We hope this book is useful to a variety of audiences. 




Other publications