A decade chasing how things hang together.

My most recent work studied self-avoiding trails — paths on a lattice that may revisit a vertex but never re-use an edge. Looking at their critical behaviour turned up some surprises: the collapse of trails in three dimensions shows a non-standard scaling that no theory yet predicts, and the phase diagram shifts in interesting ways once you add stiffness or nearest-neighbour interactions. The same intersecting-path geometry underlies problems as far afield as the Anderson metal–insulator transition, and characterising the collapse transition of trails is still considered an open problem in the field.

I built an algorithm for the Tutte polynomial of a graph that extends the classic transfer-matrix approach with the computer-science idea of tree-decomposition. The result was two-fold: a software package faster than anything else available (published through Zenodo, DOI 10.5281/zenodo.15941), and a general framework that adapts to many other graph polynomials — letting researchers state and test conjectures about chromatic-polynomial roots in a fraction of the time.

My PhD used a fermionic (Grassmann) formalism to count forests on graphs and, more generally, hypergraphs. I proved that the asymptotics depend on the ratio of trees to vertices, giving rise to a phase transition — one that turns out to be the spontaneous breaking of a hidden supersymmetry, and the appearance of a “giant component.”