I hold a Daphne Jackson Fellowship, sponsored jointly by Swansea University and the EPSRC.
Most of my work is in the area of Alexandrov geometry, the study of inner metric spaces with a lower curvature bound. I am interested in this subject both for its own intrinsic beauty and for the light it can cast on Riemannian geometry. I also study symmetry in a wide variety of settings – general topological spaces, metric spaces, Alexandrov spaces and Riemannian manifolds.
I am applying my geometric expertise to topological data analysis, taking on questions of geometric inference. In particular, I am studying the construction of estimators for geometric invariants of submanifolds of Euclidean space.