Speaker: Victor Turchin (KSU)

This talk is a warm up for the next week talk "Binomial rings and homotopy theory" by Geffroy Horel. The goal is to recall how the rational homotopy theory recovers in a fully faithful manner the rational homotopy type of nilpotent spaces by assigning to them dg commutative algebras.  In particular, the rational homotopy groups are recovered by the associated Harrison complex. If time permits I will speak about Comm_\infty algebras. While the structures of L_\infty and A_\infty algebras have a relatively easy description, Comm_\infty algebra structure requires the Lie cooperad, which also can be nicely described, but this description is not so well-known.