Low Rank Approximations - Numerical Approximations from Algebraic Geometry

We consider the problem of approximating functions defined on very large numerical grids or meshes. This is a basic computational problem which arises in numerous modeling contexts, ranging from chemistry to biology to statistics. In this talk, we consider some relatively new approximation schemes based on the algebra and geometry of tensors. We will give several illustrative examples of this approach, and indicate some open problems which may be of interest to algebraic geometers.