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Marie Brandenburg: How to slice a polytope

Speaker: Marie Brandenburg (KTH)

Combinatorics Seminar

Time: Wed 2024-03-13 10.15 - 11.15

Location: Room 3721

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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.