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**0:14:50**
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The Johnson homomorphism. In the Artin case, this is the action of the Drinfel'd-Kohno Lie algebra on the free Lie algebra.

**0:22:55**
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This seems to be the theorem on page 7 of

Kawazumi's notes. The completion $\widehat{{\mathbb Q}\pi}$ is relative to powers $(I\pi)^p$ of the augmentation ideal. The completion $\widehat{{\mathbb Q}\hat\pi}$ is relative to ${\mathbb Q}{\mathbb 1}+|(I\pi)^p|$.

**0:31:06**
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$\tau(t_C) = L(C) = \left|\frac12(\log x)^2\right|$

**0:34:32**
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Proof of $\tau(t_C) = L(C) = \left|\frac12(\log x)^2\right|$.

**0:42:52**
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Given a symplectic expansion $\theta$...

**0:50:55**
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$\delta\circ\tau=0$, part II. What's the geometry behind this?

**0:57:52**
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Is there $\theta$ such that $\delta^\theta=\delta^{alg}$?