Moduli spaces of nodal curves from homotopical algebra

I will explain how the Deligne-Mumford compactifications of moduli spaces of curves (of all genera) arise from the moduli spaces of framed curves by homotopically trivializing certain circle actions in an appropriate sense. I will sketch how this is relevant to the problem of relating GW invariants (in all genera) with Fukaya categories. A variation of this description gives rise to a partial compactification of moduli spaces of curves. Time permitting, I will talk about some work in progress on using it to define new operations on Rabinowitz Floer cohomology and positive symplectic cohomology.