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. Harvey, J. G-actions with close orbit spaces Transformation Groups 22 4 967 977
  2. Harvey, J., Searle, C. Orientation and symmetries of Alexandrov spaces with applications in positive curvature The Journal of Geometric Analysis 27 2 1636 1666
  3. Harvey, J. Convergence of isometries, with semicontinuity of symmetry of Alexandrov spaces Proceedings of the American Mathematical Society 144 8 3507 3515
  4. Harvey, J. 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.