Supermodular Operads

The modular operad encodes in a combinatorial way how nodal curves in the boundary of the moduli space of stable curves can be obtained by glueing smooth curves along marked points. In this talk, I will present a generalization of the modular operad to moduli spaces of SUSY curves (or super Riemann surfaces). This requires colored graphs and generalized operads in the sense of Borisov-Manin.