Abstract: Many problems in science can be described by polynomial equations. The solution set of the corresponding polynomial system is referred to as an algebraic geometrical model for the problem. When the solution set consists of isolated points the model is easy to describe and even to visualise.

For higher dimensional solution spaces, deeper and more sophisticated geometrical and numerical techniques are required. I will present some ideas on algebraic sampling.

The key challenge is to estimate the right density to recover the topological signature of the model. Classical geometrical tools have shown to be effective and essential for algebraic analysis of data.