Sebastian Seemann | Vandermonde cells as positive geometries 

Amplituhedra, Cluster Algebras, and Positive Geometry Conference
May 31, 2024
Speaker: Sebastian Seemann, KU Leuven
Title: Vandermonde cells as positive geometries
Abstract: Vandermonde cells represent semialgebraic subsets of R^n, characterized as the image of a simplex under the Vandermonde map. However, within the realm of positive geometry, several challenges arise in establishing canonical forms for these cells. These include issues such as non-normal boundaries, non-transversal intersections, and singularities of boundary curves. Even more difficulties appear when considing the limiting Vandermonde cell, which is not semi-algebraic and thus doesn’t fit within the standard framework of positive geometries. In this presentation, I will first review the notion of Polypols and their canonical forms, examining the complexities encountered when dealing with Vandermonde cells. In particular, I will explain what goes wrong in the case of Vandermonde cells and which obstructions we can deal with.