Dr Norman Do

Research Overview

Broadly speaking, my research interests lie at the intersection of geometry, topology and combinatorics, with the problems I find most appealing arising from mathematical physics. In particular, most of my recent research has focused on the related notions of topological recursion and quantum curves. Topological recursion is a particular structure that emerged from the mathematical physics literature a little more than a decade ago and has since received a great deal of attention. It is now known or conjectured to govern a vast array of problems, including: the enumeration of graphs on surfaces, factorisations in symmetric groups, matrix models, intersection theory on moduli spaces, Gromov-Witten theory, cohomological field theories and quantum invariants of knots.

Selected Publications

[1] Borot, Gaëtan ; Charbonnier, Séverin ; Do, Norman ; Garcia-Failde, Elba. "Relating ordinary and fully simple maps via monotone hurwitz numbers". In: Electronic Journal of Combinatorics. 2019 ; Vol. 26, No. 3. pp. 1-24.

[2] Do, Norman ; Norbury, Paul. "Pruned hurwitz numbers". In: Transactions of the American Mathematical Society. 2018 ; Vol. 370, No. 5. pp. 3053-3084. https://doi.org/10.1090/tran/7021

[3] Do, Norman ; Manescu, David. "Quantum curves for the enumeration of ribbon graphs and hypermaps". In: Communications in Number Theory and Physics. 2014 ; Vol. 8, No. 4. pp. 677 - 701.

[4] Do, Norman ; Norbury, Paul Timothy. "Counting lattice points in compactified moduli spaces of curves". In: Geometry and Topology. 2011 ; Vol. 15. pp. 2321 - 2350. https://doi.org/10.2140/gt.2011.15.2321

[5] Do, Norman ; Norbury, Paul Timothy. "Weil-Petersson volumes and cone surfaces". In: Geometriae Dedicata. 2009 ; Vol. 141, No. 1. pp. 93 - 107. https://doi.org/10.1007/s10711-008-9345-y