Speaker: Annika Burmester (Nagoya Univ.)
Title: Algebraic relations between multiple Eisenstein series
Abstract: In 2006, Gangl, Kaneko, and Zagier introduced multiple Eisenstein series as a generalization of classical Eisenstein series. Their constant Fourier coefficients are multiple zeta values, offering deeper insights into the relationship between these two types of objects. We want to describe the rational algebraic relations among multiple Eisenstein series. As a first step, we introduce a combinatorial version of them, which is essentially constructed by replacing the Fourier coefficients by a rational solution of the double shuffle relations. Inspired by Racinet’s work on formal multiple zeta values, we study the relations among combinatorial multiple Eisenstein series modulo products in terms of non-commutative polynomials. Precisely, we present a vector space bm_0 extending Racinet’s double shuffle Lie algebra dm_0. We propose a Lie bracket on bm_0, derived from a post-Lie structure and generalizing the Ihara bracket.