Chiara Meroni: Polytopes and their intersection buddies

Abstract

Intersection bodies are a popular construction in convex geometry. We will analyze some of their interesting features and then focus on the intersection bodies of polyotopes. They are always semialgebraic sets and are naturally related to zonotopes, which somehow describe their boundary structure. We will explore this connection via some examples and explain the ideas behind the main results. This is based on a joint work with Katalin Berlow, Marie-Charlotte Brandenburg and Isabelle Shankar.

Reference

Katalin Berlow, Marie-Charlotte Brandenburg, Chiara Meroni, and Isabelle Shankar. Intersection bodies of polytopes. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, January 2022. https://arxiv.org/abs/2110.05996