| Résume | We review the Kashiwara-Vergne problem and its relation to the theory of Drinfeld associators. In this context, one interesting result is an upper bound on the Grothendieck-Teichmueller Lie algebra $grt_1$ coming from the Kashiwara-Vergne theory. It should be compared with the upper bound coming from the theory of multiple zeta values. We also apply our technique to Rouvière's theory of symmetric spaces. In particular, we show that the e-function of Rouvière can be viewed as a map from the set of even associators to the vector space of anti-cyclic words in two letters (e.g. $str(xy)=-str(yx)$). We conjecture that this map is injective. The talk is based on joint works with C. Torossian, B. Enriquez, M. Podkopaeva and P. Severa. |
