QM Research Seminar: Brunnian braids and the inclusion from double shuffle Lie algebra to Kashiwara--Vergne Lie algebra

Speaker: Muze Ren (​University of Strasbourg).

Abstract: 
​Multiple zeta values (MZVs) are real numbers that generalize Riemann zeta functions at integer values. MZVs have three distinguished set of relations, namely the stuffle relation, shuffle relation and regularization relations, those relations has deep connection with the theory of motives. G. Racinet introduced the double shuffle Lie algebra (dmr_0)  and use it to study formally those three set of relations. Kashiwara-Vergne Lie algebra (krv_2) was introduced by A. Alekseev and C. Torossian when they give a proof of Kashiwar--Vergne conjecture in Lie theory.

In this talk, I want to use the notion of Brunnian braids to give a topological description of dmr_0 and symmetric krv_2.   And prove that dmr_0 injects to symmetric krv_2. This talk is based on the preprint arXiv:2605.20844 [math.QA] and arXiv:2607.28163 [math.QA].