My main field of research is statistical mechanics, which is the study of physical systems with many, many constituents, with the goal of understanding how these constituents can cooperate to bring about global changes of state, otherwise known as phase transitions. Typical examples of phase transitions are liquid water freezing, or boiling, or a magnet losing its magnetic field when it's heated.
Currently, my primary research focus is the development of efficient computer implementations of Monte Carlo sampling algorithms, starting with self-avoiding walks and related models of polymers. Significant progress is possible for a wide range of applications, both in the field of statistical mechanics (percolation, Hamiltonian paths, hard spheres) and more broadly (exotic option pricing), for which either simple sampling or Markov chain Monte Carlo is the state of the art.
I also have research interests in developing efficient enumeration algorithms, physical combinatorics, climate science, modelling more broadly, polymer physics, and mathematical visualisation.