Chow quotients: from matroids to tensors

In his groundbreaking work, June Huh associated to a representation of a matroid a subvariety of a permutohedral variety or of a product of projective lines. This construction, among others, allows one to prove the log-concavity of the chromatic polynomial of a graph. As already observed by Billera and Sturmfels, the relation between the product of projective lines and the permutohedral variety is obtained via the Chow quotient. In our talk, we show how this construction is related to tensors, Grassmannians, and varieties of complete quadrics and complete collineations.