Taking a Step from the Waring Rank Toward the Chow Rank

The main goal of this talk is to present a result related to a conjecture suggested by Catalisano, Geramita, and Gimigliano in 2002, which claims that the secant varieties of tangential varieties to Veronese varieties are non-defective modulo a few known exceptions. This is joint work with Nick Vannieuwenhoven.