On cutting planes for Mixed Integer Programming

This talk gives an introduction to a recently established link between the geometry of numbers and mixed integer linear optimization. The main focus is to provide a review of families of lattice-free polyhedra and their use in the context of deriving and explaining cutting planes for mixed integer programs. This approach is not only mathematically interesting, but it leads to some fundamental new discoveries, such as an understanding under which conditions cutting planes algorithms converge finitely. These theoretical results suggest the possibility that cutting planes from special families of lattice-free polyhedra could give rise to efficient novel algorithms.