Passare's conjecture on solid amoebas of maximally sparse polynomials

Let $p(z)$) be a maximally sparse polynomial, meaning that the support of $p$ is equal to the set of vertices of its Newton polytope. The Passare conjecture. The amoeba of $p(z)$ is solid.

Here, an amoeba is the image of the zero set of a Laurent polynomial under the coordinatewise logarithm of absolute values, and a solid amoeba is one whose complement has the minimal possible number of connected components, namely the number of vertices of its Newton polytope. The conjecture concerns the relation between the sparsity of a polynomial and the topology of its amoeba complement; its status is not established by the supplied source.