Degeneration of Mixed Elliptic motives and depth filtration of multiple zeta val

任课教师 Speaker:Tomohide Terasoma
时间 Time: 每周二、周四13:30-15:05,2019-8-6 ~ 8-15
地点 Venue:清华大学近春园西楼第三会议室

课程描述 Description

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.

预备知识 Prerequisites

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

参考资料 References