Rational Embedding calculus via Frobenius algebras

Results of Campos-Willwacher, Idrissi, Willwacher and using results of Lambrechts-Stanley, show that rationally the spaces of configuration of points on a (framed) manifold, seen as a right module over the E_d operad, is the same as a dg Frobenius algebra, at least in the simply connected case. We will see that the same is true in families. More precisely, we will see that the E_d operad is "half Koszul dual" to the involutive (non counital) Frobenius properad. From this we obtain an equivalence between the moduli spaces (or infty-categories) of right E_d modules of configuration space type and involutive Frobenius algebras.
This is joint work with Thomas Willwacher.