Mathematics

Matrix models and combinatorial description of moduli spaces of Riemann surfacesAbstract: The rigorous study of moduli spaces of open Riemann surfaces has been initiated by Pandharipande, Solomon and Tessler. After a review of matrix and combinatorial models describing intersection theory on the moduli spaces of closed Riemann surfaces (Deligne-Mumford moduli spaces) I will introduce their generalization to the open case.Main references:Kontsevich - Intersection theory on the moduli space of curves and the matrix Airy functionPandharipande, Solomon, Tessler - Intersection theory on moduli of disks, open KdV and VirasoroSafnuk - Combinatorial models for moduli spaces of open Riemann surfaces