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.

Areas of Expertise

  • Geometry
  • Topology
  • Topological data analysis

Publications

  1. G-actions with close orbit spaces. Transformation Groups 22(4), 967-977.
  2. & Orientation and symmetries of Alexandrov spaces with applications in positive curvature. The Journal of Geometric Analysis 27(2), 1636-1666.
  3. Convergence of isometries, with semicontinuity of symmetry of Alexandrov spaces. Proceedings of the American Mathematical Society 144(8), 3507-3515.
  4. Equivariant Alexandrov geometry and orbifold finiteness. The Journal of Geometric Analysis 26(3), 1925-1945.

Teaching

  • MA-004 Fundamental Geometry

    This module introduces some essential geometric tools covering the basics of trigonometry, coordinate geometry, vectors and matrices.