Passare–Rullgård's conjecture on maximally sparse Laurent polynomials

A Laurent polynomial is maximally sparse when its support consists of the vertices of its Newton polytope. Its amoeba is solid when its complement has the minimal possible number of connected components, namely the number of vertices of the Newton polytope.

Passare–Rullgård's conjecture. A maximally sparse Laurent polynomial has a solid amoeba.

This conjecture concerns the relationship between the combinatorial sparsity of a Laurent polynomial and the topology of its amoeba. The supplied text does not state whether the conjecture has been proved or disproved.