Positive Toric Geometry
On August 16-17, 2023, I will teach a minicourse on positive toric geometry at the Hypergeometric school in Kobe, Japan. Here is the short description:
We study the positive and nonnegative points of affine and projective toric varieties, embedded via a monomial parametrization. We prove the well-known fact that a nonnegative toric variety is homeomorphic to a cone, in the affine case, or a polytope, in the projective case. We establish this via the algebraic moment map. We discuss applications of positive toric varieties in algebraic statistics, linear programming and geometric modelling.
A first draft of the lecture notes can be downloaded here: