  We study the supersymmetric circular Wilson loops of N=4 super Yang-Mills in
large representations of the gauge group. In particular, we obtain the spectral
curves of the matrix model which captures the expectation value of the loops.
These spectral curves are then proven to be precisely the hyperelliptic
surfaces that characterize the bubbling solutions dual to the Wilson loops,
thus yielding an example of a geometry emerging from an eigenvalue
distribution. We finally discuss the Wilson loop expectation value from the
matrix model and from supergravity.
