Our reseach group works in the field of applied and computational topology and geometry. The focus lies on questions regarding the connectivity of data on multiple scales. This is global information, concerning the data as a whole, and inaccessible by standard means of data analysis. Popular methods in this context are persistent homology, Vietoris–Rips complexes, and Delaunay complexes (Alpha shapes).
We consider theoretical questions, such as the stability of persistence barcodes or connections to representation theory, but also computational problems, such as finding the Vietoris–Rips persistence barcode of a set of points. We study the hardness of certain computational problems arising in applied topology, and develop fast code that is widely used in applications (http://ripser.org).