Marie Brandenburg: How to slice a polytope

ABSTRACT: Given a 3-dimensional cube, the intersection with an affine hyperplane is always a polygon with 3,4,5, or 6 vertices. But how can one understand the slices of a general polytope? And which slice is “the best”, for example, is the slice of maximal volume?

In this talk, we consider the structure of all possible affine hyperplane sections of a convex polytope, and we craft algorithms that compute optimal sections for various combinatorial and metric criteria. Along the way, we will encounter a variety of famous hyperplane arrangements which will guide our algorithms.

This is based on joint work with Jesús De Loera and Chiara Meroni.