Permutation combinatorics of worldsheet moduli space

Understand

Light-cone string diagrams have been used to reproduce the orbifold Euler characteristic of moduli spaces of punctured Riemann surfaces at low genus and with few punctures.

• Nakamura studied the meromorphic differential introduced by Giddings and Wolpert to characterise light-cone diagrams and introduced a class of graphs related to this differential.
• These Nakamura graphs were used to parametrise the cells in a light-cone cell decomposition of moduli space.
• We develop links between Nakamura graphs and realisations of the worldsheet as branched covers.