TITLE: Generalized Barycentric Coordinates<br>
Speaker: Corey Irving<br>
Date:  30 October 2008<br>

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.