Exploring algebras to understand tensors

Tensor decomposition is an active research topic, with applications across a wide range of fields. In this talk, we will discuss how the problem of decomposing (totally) symmetric tensors can be translated into the construction and study of special families of algebras associated with a given tensor. I will present different approaches arising from recent and ongoing projects, ranging from linear to highly non-linear algebra.

Along the way, I will present some open questions I would like to address and mention some topics I would like to learn more about, hoping to spark discussion around these problems.