Let D be the graded Q vector space generated by motivic multiple zeta values modulo "\pi^2". The depth filtration is defined as the subspaces of $D$ generated by MZV's whose depths are less than or equal to given numbers. Broadhurst and Kreimer gave a conjecture on the two variable generating function of the dimensions of weight n and depth d parts.
In this conjecture, the dimensions of elliptic cusp forms appears,which suggests the existence of an influence of mixed elliptic motives on mixed Tate motives.
In this lecture, we gave a relation between the fundamental group of the degenerating elliptic curve and that of the projective line minus three points.
To give a clear explanation for the relation with the relative bar complex,
we introduce a certain resolution, called a sandwich resolution of a dual free associative algebra which yields the generating function conjectured by Broadhurst and Kerimer.

Hodge structure and multiple zeta values. Comohology of the moduli space of eliipic curves