Comparison between cuspidal generators on the depth-graded motivic Lie algebra and on the linearized double shuffle Lie algebra

According to the Broadhurst-Kreimer conjecture, there are modular phenomena in the ring of multiple zeta values
with the depth filtration. The goal of this project is to give a substantial solution to the Broadhurst-Kreimer conjecture in depth 4. In this talk, I will describe a conjectural connection, which involves a ratio of critical values of the L-function
of a cusp form, between two different cuspidal generators constructed by F. Brown and present an attempt and some results to reveal the connection. This talk is based on a joint work with Seidai Yasuda (advised by Francis Brown).