As noted long ago by Atiyah and Bott, the classical Yang-Mills action on a Riemann surface admits a beautiful symplectic interpretation as the norm-square of the moment map associated to the Hamiltonian action by gauge transformations on the affine space of connections. In this talk, I will explain how certain Wilson loop observables in Chern-Simons gauge theory on a Seifert three-manifold can be given an analogous symplectic interpretation. Among other consequences, this fact implies that the stationary-phase approximation to the Wilson loop path integral is exact for torus knots, an observation made empirically by Lawrence and Rozansky prior to this work.