Lattice points in compactified moduli spaces of curves and topological recursion
Moduli spaces of curves are fundamental objects, appearing in geometry and mathematical physics. In previous work with Paul Norbury, we define the notion of lattice points in compactified moduli spaces of curves and prove that their enumeration leads to polynomials whose top and bottom degree coefficients store interesting geometric information. This leads to two natural questions: does the enumeration satisfy the so-called topological recursion and do the intermediate coefficients possess a geometric interpretation? In recent work with Anupam Chaudhuri and Ellena Moskovsky, we answer the former question in the affirmative, which should provide a first step on the path to answering the latter.
Dr Norm Do, Monash University