Title: Ideals of Geometrically Characterized Point Sets and Simplicial Complexes

Abstract: Let X be a finite set of points in an affine space. A Lagrange polynomial for X is a polynomial which vanishes at all but one of the points of X. In a way which can be made precise, not every point set admits Lagrange polynomials, but the existence of Lagrange polynomials for X guarantees that a polynomial function is completely determined by its values on X. If in addition, these Lagrange polynomials fully factor into products of linear polynomials, the set X is called geometrically characterized. In this talk, we will discuss the geometry of geometrically characterized sets, the ideals of such point sets, and will make some connections to simplicial complexes