Genus zero curves and Koszul duality

Abstract: 

The collection of genus zero stable curves forms an operad by gluing at the marked points. We construct an explicit cellular decomposition compatible with the gluing, that on the chain level is the bar construction of a small operad model for chains on the open moduli space. This upgrades a duality constructed originally by Getzler in homology between the gravity and the hypercommutative operads, and is joint work with Tommaso Rossi.