All talks will take place in the HMI Seminar Room at the Hamilton Mathematics Institute
I will show how polylogarithms arise in Feynman diagrams, and discuss how physicists make use of their algebraic properties (symbol, coaction) with a view to confronting more complicated iterated integrals.
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. G. Racinet introduced the double shuffle Lie algebra (dmr_0) and use it to study formally those three set of relations. The symmetric Kashiwara-Vergne Lie algebra (krv^{sym}_2) was introduced by A.~Alekseev and C.~Torossian in their study of Kashiwara--Vergne conjecture in Lie theory.
In this talk, I want to present a self contained (as much as I can) proof of the injection from dmr_0 into the krv^{sym}_2. The talk is based on the recent preprint arXiv:2607.28163 [math.QA] and ealier work of L.~Schneps and B.~Enriquez--H.~Furusho.