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.