Research

Geometry of moduli spaces

My doctoral work at the University of Melbourne constructed canonical cell decompositions of the moduli and Teichmüller spaces of genus-two Riemann surfaces, using Delaunay and Voronoi decompositions defined by Weierstrass points. My current work revisits and extends these results, drawing on circle patterns and the combinatorics of Whitehead moves.

Algorithms on surfaces

I study minimum k-cut problems for graphs embedded on surfaces, building on the work of Chambers, Erickson, Fox and Nayyeri.

Mathematical oncology

I work on structured population models of tumour dynamics and on a polytope-based geometric framework for cancer-cell migration and metastasis. I am also helping develop a mathematical oncology programme at Fiji National University.

Imaging

Motion estimation in single-pixel imaging, in collaboration with engineers at the University of Waikato.

Publications

• Weierstrass Points and Canonical Cell Decompositions of the Moduli and Teichmüller Spaces of Riemann Surfaces of Genus Two
  PhD thesis, University of Melbourne, 2007.