Intersection Bodies of Polytopes

Intersection bodies are classical objects from convex geometry. But using tools from combinatorics and real algebraic geometry, what more can we say about these objects?

In this talk we show that the intersection body of a polytope is always semialgebraic. Moreover, we compute the irreducible components of the algebraic boundary and provide an upper bound for their degree. This is joint work with Katalin Berlow, Chiara Meroni and Isabelle Shankar.