Speaker: Amitabh Basu
Title: Cutting Planes and Geometry of Numbers
Abstract: We survey some recent results in cutting plane theory for integer programming. Cutting Planes give a way to reduce the search space for the optimal solution in an integer optimization problem. The results we will present are very recent connections between cutting planes and covering/tiling properties of subsets of euclidean sets. Important structural information about cutting planes can be translated to geometric questions like: Does a particular compact subset B of R^n cover all of R^n when we consider all of its translates by integer vectors. This connects to very classical problems in the geometry of numbers and deep theorems like the Venkov-Alexandrov-McMullen theorem on tilings, and the geometry of zonotopes can be leveraged. Research in this area of integer optimization is very much work-in-progress; we will close the presentation with an invitation to join our quest with some open problems.