Professor Brock’s work to date has been in the area of geometry and topology, the mathematical study of shapes. He studies coarse features of a space that can determine its structure, using these notions with his collaborators to classify spaces called hyperbolic 3-manifolds. His interests focus on parameter spaces of geometric structures, on surfaces, and on 3-manifolds, and more recently have shifted to the study of finite metric spaces or "point clouds" whose geometry and topology has found new applications in the area of Topological Data Analysis. Understanding the "shape" of data has become a powerful tool for understanding its structure and what meaning can be derived from how data sets are clustered and arranged.
Director, Data Science Initiative