Deligne and Goncharov (2005) constructed a neutral tannakian category of mixed Tate motives unramified over Z[mu_N,1/N]. The periods of the category contain the N-cyclotomic multiple zeta values (MZVs). When N = 1, Gangl–Kaneko–Zagier (2005), Pollack (2009), Hain–Matsumoto (2014), and Brown (2017) have shown relations between MZVs are induced by cusp forms of SL_2(Z). We hope to understand the analogous role of level N cusp forms in relations between N-cyclotomic MZVs when N > 1.

I will share my progress on this problem using the elliptic KZB connection over the full level N universal elliptic curve. At the singular fiber above a distinguished cusp, the connection degenerates to the motivic fundamental group of P^1 - {0,mu_N,infty} studied by Deligne and Goncharov. This observation enables us to compute the first order motivic Galois action on the unipotent fundamental group of the Tate elliptic curve with N punctures, a mixed Tate motive whose periods are spanned by the N-cyclotomic MZVs.