(Warning: The speaker is not a category theorist. The talk will feature abstract algebra, at least one functor, and touch on operads if time allows.) The Goldman-Turaev loop operations equip the vector space of free loops in a surface with boundary with the structure of a Lie bialgebra. In this talk we will construct a "homomorphic expansion" (or "formality map") for the Goldman-Turaev Lie bialgebra: an isomorphism between the I-adic completion and the associated graded Lie algebra. After an introduction to expansions, we will show that in genus zero the Goldman-Turaev loop operations are naturally induced by tangle operations in the surface cross an interval. In turn, the Kontsevich integral of tangles induces a homomorphic expansion for the Goldman-Turaev Lie bialgebra. This is especially interesting in light of a seminal result of Alekseev, Kawazumi, Kuno and Naef stating that in genus zero Goldman-Turaev expansions correspond to solutions to the Kashiwara-Vergne equations arising from convolutions on Lie groups, opening up rich connections to quantum algebra. Our results are parallel to earlier work of Massuyeau (in the context of braids) and Alekseev-Naef (in the context of the KZ connection), and related to recent results on 'emergent' objects by Kuno and Ren. I will discuss outstanding questions and work in progress at the end. Based on joint work (link) with Dror Bar-Natan, Jessica Liu, Tamara Hogan, and Nancy Scherich.