Secant and Tangential Varieties of Segre-Veronese Varieties

Secant and tangential varieties of homogeneous varieties are of great interest both in pure and applied mathematics. Classically, they are studied using representation theory. We would like to present another, new method based on a change of coordinates, inspired by algebraic statistics. It reveals connections of the secant and tangential variety of Segre-Veronese varieties to toric geometry. In particular, it allows to apply easy combinatorial methods to study their geometry - e.g. the singular locus, type of singularities. The talk will contain results from a joint work with Manivel and Oeding, Zwiernik and is based on previous results of Sturmfels and Zwiernik.