Title: Flat connections and quantum groups
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Abstract: I will explain how quantum groups can serve as natural
receptacles for the monodromy representations of certain flat
connections arising from representation theory. This will be
illustrated through two main examples: the Knizhnik-Zamolodchikov
equations, whose monodromy gives representations of Artin's braid
groups and the Casimir connection, which gives rise to representations
of the generalised braid groups associated to simple Lie algebras.