Professor Paul Fendley works on statistical mechanics, studying the collective behaviour of systems with many particles. He typically analyses systems with strong interactions, making use of a variety of powerful mathematical tools. One such tool is integrability, which takes advantage of a panoply of symmetries constraining the system. Another is supersymmetry, famous in particle physics, which yields interesting special properties in some intriguing condensed-matter systems. Field theory underlies much of theoretical physics, with one particular focus in Fendley's work being those with conformal symmetry. These methods of strongly interacting statistical mechanics provide essential tools for analysing condensed matter.