On the irrationality of certain coefficients of the Alekseev-Torossian   associator
  We give explicit formulas for the first few coefficients of the Alekseev-Torossian associator and a second Drinfeld associator. This is done by analyzing the free and transitive action of the Grothendieck-Teichm\"uller group and its Lie algebra $\mathfrak{grt}_1$ on the set of Drinfeld associators. As a result we obtain that, up to a conjecture on multiple zeta values, both associators are not rational. 
Matteo Felder
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