Regularity regimes for symmetric tensor decomposition

Additive decompositions of tensors play a major role in addressing both theoretical and practical problems. To a given tensor, one can canonically associate a numerical quantity, called the rank, which measures the tensor complexity and encodes some of its intrinsic properties.

It is commonly believed that the higher the rank, the more difficult it is to compute minimal tensor decompositions.

In this talk, we consider the class of symmetric tensors and present an algebraic method for computing their decompositions and rank. We show that the complexity of this approach is not directly dependent on the rank of the considered tensor, but rather on the regularity of minimal geometric objects one can associate with it.