Interpolation, Approximation, and Algebra

Abstract

This report involves two concepts of geometric modeling: multi-variate data interpolation by polynomials, and the study of generalized bary\-centric coordinates. These topics are connected to a wide range of of applications, from computer aided design (CAD) systems for designing airplanes and automobiles to animation in movies to problems in numerical analysis and partial differential equations. Traditionally these topics were studied mostly from an analytic standpoint, but recently advanced algebraic tools have come into the picture. The purpose of the mini-workshop was to bring together a diverse group of researchers with different areas of expertise, drawing from both the approximation theory and algebraic geometry communities, and to explore the connections between the two areas in greater detail.