Speaker
Description
The goal of this talk is to explain the mechanism by which cusp forms of certain congruence subgroups of SL2(Z) impose relations in the depth filtration of the motivic fundamental group of the category of mixed Tate motives unramified over the ring Z[muN,1/N]. The known depth 2 relations in the case N=1, first observed by Ihara and Takao, were proved by Francis Brown and Hain--Matsumoto. (Both proofs use a period computation due to Brown). One should be able to similarly establish depth 2 relations when N is a prime number > 5. The first steps towards this goal were taken by Eric Hopper in arXiv:2208.01153 using the elliptic KZB connection for the universal family of elliptic curves with a cyclic subgroup of order N removed, which was written down by Calaque and Gonzalez. I will explain his work and how it isolates the period computations that control the relations.
