Operadic structures in the moduli space of curves
In this talk, I will illustrate a new algebraic structure arising in the moduli space of Riemann surfaces. I will focus primarily on an example construction that can be thought of as the mirror symmetric dual to the Catalan numbers, but will also discuss related examples that involve the symplectic and hyperbolic structures on the moduli space of Riemann surfaces. All of these rather different constructions, plus many others, are unified by the structure of a topological recursion operad, which is a construction with close connections to the theory of Eynard-Orantin recursion.