My research interests lie in geometry and topology. The problems I find most appealing are those which have a combinatorial flavour and connections with mathematical physics.

My doctoral research has focused on moduli spaces of curves. These spaces parametrize algebraic curves, and their geometry captures the way in which algebraic curves vary in families. Over the past few decades, moduli spaces of curves have become tremendously important in mathematics. Much research has centred on their intersection theory, which has an incredible structure and is intricately related to a variety of fields, such as geometry, combinatorics, integrable systems and theoretical physics. Recent results of Mirzakhani provide an explicit connection between this intersection theory and volumes of moduli spaces. My thesis shows that these volumes satisfy interesting new identities which emerge from the geometry of hyperbolic cone surfaces. I also give a new approach to Kontsevich's combinatorial formula, one of the main ingredients in his proof of Witten's conjecture. Due to the abundance of deep conjectures and connections to other fields, it is a very exciting time to be working in this area.

At this formative stage of my career, I am keen to expand my mathematical repertoire to include other avenues of research. For example, I am also interested in modern knot and manifold invariants and their relations to other parts of mathematics.