## Seminar:

Fall 2008, Thursdays, Milner 216, 4:00-4:50 PM
__ Date:__ ** October 30 **

**" Generalized Barycentric Coordinates "**

**Corey Irving**

__Abstract__The goal of this talk is to extend the notion of barycentric coordinates of simplices to arbitrary polytopes and to describe the algebraic varieties that these coordinates define. I will define what barycentric coordinates are for simplices and point out some of the properties they have. There are several ways to extend the idea of barycentric coordinates to polytopes which preserve some or all of these properties, we will focus on one called Wachspress coordinates. These generalized barycentric coordinates will be rational functions of the points of the polytope and as such can be viewed as a parametrization of some algebraic variety. We will discuss how to obtain the implicit equations of this variety using just the most basic information of the polytope (vertices, facets, etc). Backgound assumed for this talk is minimal. I aim to keep this talk simple and short.