Secant varieties to tangential varieties of cubic Veronese embeddings.

The past several decades have seen an interest in secant varieties cross an ever widening collection of desciplines including algebraic complexity theory, algebraic statistics, interpolation as well as algebraic geometry. A well known classification of defective secant varieties of Veronese varieties has been completed in a series of papers by Alexander and Hirschowitz. There is a conjecturally completed list of defective secant varieties to tangential varieties of Veronese varieties suggested by Geramita, Catalisano and Gimigliano. In this talk, I will discuss an inductive approach to establish the existence of large classes of non-defective secant varieties to tangential varieties of cubicc Veronese embeddings. This approach was inspired by the work of Brambilla and Ottaviani.