Positive Geometry and Wonderful Polytopes

A positive geometry is a certain type of space that is equipped with a canonical meromorphic form. While the construction originates in theoretical physics, many beloved objects in algebraic combinatorics and geometry turn out to be examples of positive geometries. In this talk, I will focus on one such example: polytopes. Given any convex polytope, we will study its corresponding “wonderful” polytopes, which arise from the wonderful compactification of a hyperplane arrangement in the same way that polytopes arise as the regions of a hyperplane arrangement. I will describe on-going work with Chris Eur, Lizzie Pratt, and Raluca Vlad showing that any simple wonderful polytope is a positive geometry. I aim to make this talk accessible, and no prior knowledge of positive geometries or wonderful compactifications will be assumed.