Title:  On lattice polytopes, convex matroid optimization, and degree sequences of hypergraphs

We introduce a family of lattice polytopes, called primitive zonotopes, which can be seen as a generalization of the permutahedron. We discuss connections to the largest diameter of lattice polytopes and to the computational complexity of multicriteria matroid optimization. Tightening of the bounds for the largest possible diameter of a lattice polytope, complexity results, and open questions are presented. In particular, we answer a question raised in 1986 by Colbourn, Kocay, and Stinson by showing that deciding whether a given sequence is the degree sequence of a 3-hypergraph is computationally prohibitive. Based on joint works with Asaf Levin (Technion), George Manoussakis (Paris Sud), Syed Meesum (IMSc Chennai), Shmuel Onn (Technion), and Lionel Pounin (Paris XIII).