Title: What is a Spline? Applications of Commutative Algebra to Approximation Theory.

Abstract: Splines are piecewise polynomial functions of a given order defined on a triangulated (or polyhedrally subdivided) region in R^d. They are 
used in geometric modelling, approximation theory and solving PDEs. Also, one would be surprised at the amount of commutative and homological algebra 
used in studying splines. Our goal will be to discuss and understand three ways the space of splines over a given region may be identified.