University Seminar- Computability, Complexity, and Algebraic Structure: Barycentric algebras and barycentric coordinates

Time: Wednesday, March 26, 1:00 – 2:00pm

Place: Phillips Hall 110

Speaker: Anna Zamojska-Dzienio, Warsaw University of Technology, Warsaw, Poland

Title: Barycentric algebras and barycentric coordinates

Abstract:  Real convex sets can be presented algebraically with binary operations given by weighted means, the weights taken from the (open) unit interval in the real numbers. The class of convex sets is defined logically by certain implications, and generates the equationally-defined class of barycentric algebras.
Barycentric coordinates provide solutions to the problem of expressing an element of a compact convex set as a convex combination of a finite number of extreme points of the set. They have been studied widely within the geometric literature, typically in response to the demands of numerical analysis and computer graphics. In this talk we bring an algebraic perspective to the problem, based on barycentric algebras. We present some recent results obtained together with A. Romanowska (Warsaw University of Technology) and J.D.H Smith (Iowa State University)