My research interests lie broadly under geometric group theory and low-dimensional topology, with connections to hyperbolic geometry, computational topology, and dynamical systems. I am interested in questions regarding combinatorial complexes such as the curve complex, mapping class groups, Teichmueller space, flat surfaces, hyperbolic 3-manifolds, and CAT(0) cube complexes.
My papers on the arXiv can be found here.
Cubical geometry in the polygonalisation complex (with Mark Bell and Valentina Disarlo).
Preprint, December 2016 (PDF).
Veech surfaces and simple closed curves (with Max Forester and Jing Tao).
Accepted in Israel Journal of Mathematics.
Preprint, May 2016 (PDF).
Shadows of Teichmüller discs in the curve graph (with Richard Webb).
Accepted in International Mathematics Research Notices.
Preprint, revised December 2015 (PDF).
Projections in the curve complex arising from covering maps.
Accepted in Pacific Journal of Mathematics.
Preprint, October 2013 (PDF).
The curve complex and covers via hyperbolic 3-manifolds.
Geometriae Dedicata, December 2012, Volume 161, Issue 1, pp 233-237,
Preprint, April 2011 (PDF).
Covering maps and hulls in the curve complex
Contains material from items 1 and 2.
June 2013 (PDF).
A Python script for producing realisation graphs for systems of curves and arcs on a surface.