Pierpaola Santarsiero (Università di Bologna)

Abstract: Given a nondegenerate projective variety X, a set of r smooth points of X belongs to the r-Terracini locus of X if the span of the r tangent spaces of X at these points is linearly dependent. 
Born from the desire of understanding the behavior of non generic points, the Terracini locus of a variety is more than just a interesting purely geometric object. Specifically, in the context of tensor decomposition this object share a deep connection with condition numbers. As a consequence, Terracini loci of tensor-related varieties play a crucial role when measuring the sensitivity of a tensor rank decomposition. 
In this talk, I will introduce Terracini loci and carefully explain their connection to condition numbers in the context of tensor decomposition. I will then present some of the latest results involving these interesting objects.