Research

My research mainly concerns hyperbolic flows, particularly the knot-theoretic properties of their periodic orbits. I’ve recently also been thinking about automorphism groups in symbolic dynamics, and the effects of Ricci flow on the dynamics of geodesic flows.

Publications

  1. Distribution of periodic orbits in the homologous group of a knot complement (joint with R. Sharp), Geom. Dedicata 218, 75, 2024.
  2. Helicity, linking and the distribution of null-homologous periodic orbits for Anosov flows (joint with R. Sharp), Nonlinearity 36, 21-58, 2023.

Preprints

  1. Vassiliev invariants and writhe for periodic orbits of Axiom A flows, arXiv:2401.07940, 2024.
  2. How to hear the shape of a billiard table (joint with A. Calderon, D. Davis, J. Lanier, A. Oliveira), arXiv:1806.09644, 2018.

Thesis

On the distribution of periodic orbits and linking numbers for hyperbolic flows, University of Warwick, supervised by R. Sharp.