Wachspress Geometry

Wachspress Geometry is a young subject in the intersection of geometry, combinatorics and algebra. It is at the core of my SPP 2458 project “Wachspress Coordinates – a bridge betwen Algebra, Geometry and Combinatorics”.

Wachspress Geometry is …

• … the study of the Wachspress objects, a somewhat mysterious family of constructions on convex polytopes. Those emerge in a wide range of seemingly unrelated contexts, and the goal is to explain and exploit these connections and to work towards a unifying explanation for the ubiquity of “Wachspress phenomena”.
• … among the best understood instances of Positive Geometry. The goal is to extend tools of Wachspress Geometry to more general positive geometries.

Perhaps you have already come across some construction from Wachspress Geometry, whether in the shape of a canonical form, a stress in a framework, a model in algebraic statistics, cone volumes or volume differentials.

Below I will write an introduction to Wachspress Geometry, coming soon …

If you are interested, Rainer Sinn and I are organizing a workshop “Wachspress Geometry” in Leipzig on September 24th/25th 2024.

more coming soon …