Georgia Institute of Technology College of Sciences

Intersection bodies are a popular construction in convex geometry. I will give an introduction on these objects, convex algebraic geometry, and starshaped sets in general. Then, we will analyze some features of intersection bodies and focus on the polyotopal case. Intersection bodies of polytopes are always semialgebraic sets and they are naturally related to hyperplane arrangements, which reveal their boundary structure. Finally, we will investigate their convexity, in the two-dimensional case. The exposition will be enriched by examples and computations. This is based on joint works with Katalin Berlow, Marie-Charlotte Brandenburg and Isabelle Shankar.