David Eisenbud

Abstract:   One natural question in interpolation theory is: given a finite set of points in R^n, what is the least degree of polynomials on R^n needed to induce every function from the points to R? It turns out that this "interpolation degree" is closely related to a fundamental measure of complexity in algebraic geometry called Castelnuovo-Mumford regularity. I'll explain these ideas and some of their current interest in algebraic geometry and commutative algebra.