Universal differentials in the bar spectral sequence

The synthetic analogue of the bar comonad controls the universal differentials in the bar spectral sequence of algebras over spectral operads. This can be viewed as a deformation of Koszul duality for such algebras. I will explain ongoing work with Burklund and Senger on identifying the universal differentials in the bar spectral sequence for spectral Lie algebras over $F_p$. This will also shed light on the mod p homology of labeled configuration spaces and $E_n$-Dyer-Lashof operations for Lubin-Tate theories via a theorem of Knudsen.