Speaker
Liam Solus, KTH Royal Institut of Technology
Abstract
Unirational varieties are ubiquitous in applied algebra since models for real-world data are often defined via rational parameterizations. One way algebra helps us understand these models is by providing techniques for recovering implicit (polynomial) equations satisfied by the image of their parameterization. Extracting implicit constraints on the model can be more or less complicated, depending on the specific parameterization. In several cases relevant to statistics, there is a combinatorial structure underlying the model’s parameterization that can be exploited. In this talk, we will discuss a technique for extracting implicit equations satisfied by unirational varieties whose combinatorial structure relates to an associated partially ordered set (poset). Using examples from statistics, we will see how the method applies to problems such as computing the linear span of the variety, identifying toric reparametrizations and finding complete implicit descriptions.