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I will explain (older) joint work with Dror Bar-Natan on the relationship between 4-dimensional knot theory and Lie theory. On the knot theory side, this involves finite type invariants of welded knotted objects, in other words, a certain class of 4-dimensional tangles. On the Lie theory side stands the Kashiwara-Vergne problem, a famous problem that was first solved, after nearly 30 years, in 2006 by Alekseev and Meinrenken. I will also aim to describe more recent efforts to connect this work to related results of Alekseev-Kawazumi-Kuno-Naef, who provide a different topological interpretation of the Kashiwara-Vergne problem in terms of homotopy classes of loops on surfaces.