The ACO Seminar (2025–2026)

We can obtain a new lattice polytope by considering the Minkowski sum of two lattice polytopes. A natural question is whether every lattice point in this sum arises as the sum of lattice points from the original polytopes. While this property fails in general, there are interesting situations where it does hold, known as the integer decomposition property for pairs of polytopes. In this talk, I will survey known results on when this property is satisfied and present aspects of my own work on this problem.