I work on statistical mechanics, studying the collective behaviour of systems with many particles. I typically analyse systems with strong interactions, making use of a variety of powerful mathematical tools. One such tool is integrability, exploiting the many symmetries of certain special systems. Another is supersymmetry, famous in particle physics, but which also occurs in an interesting way in some condensed-matter systems. Field theory underlies much of theoretical physics, with one particular focus in my work those with conformal symmetry.
These methods of strongly interacting statistical mechanics provide essential tools for analysing condensed matter. One particularly striking phenomenon needing them is when collective and microscopic behaviors are radically different, what now goes under the name of emergence. A prominent example is topological matter, where fractionalised excitations in effect split apart a system’s constituents. Another is prethermal behaviour, where a system takes essentially forever to reach equilibrium. My work continually goes back and forth between the mathematical and the physical side, as no good understanding of these phenomena comes without taking both seriously.