Abstract
Secant varieties of Segre and Segre-Veronese varieties, as well as linear systems interpolating multiple points, provide a bridge between tensor algebra and algebraic geometry and are of interest in applications.
In this talk I will introduce these objects and their dimensionality problem, and will give an overview about known results and open conjectures. I will tell about how the use of computer algebra systems such as Macaulay2 is fundamental for these questions, because computer based computations not only cover the initial cases (most of the proofs are by induction), but also help understand the general behaviour.