Toric Varieties in Algebraic Statistics and Geometric Modeling

Toric varieties are beautiful objects in Algebraic Geometry whose structure can be studied via their connection to lattice polytopes. They are also varieties that admit a simple parameterization via monomials. Their simple, yet rich structure means that they are versatile objects that appear in many applied settings. In statistics, log-linear models are toric varieties. In Geometric Modeling, the connection to polytopes is used to define bases of polynomials whose domains are lattice polytopes and which have useful approximation properties.

In this talk we explain how understanding properties of toric varieties gives insight into their practical use in Statistics and Geometric Modeling and how the toric geometry language in fact brings these two areas together.