On the Symmetric Tensors Completion Problem

The aim of this elaborate is presenting the classical symmetric tensors completion problem to an audience of graduate students. As main studying tool, we will introduce the theory of hypergraph rigidity which naturally mirrors the problem itself. This has already appeared in literature: in 2023, Cruicksand, Mohammadi, Nixon, and Tanigawa introduced organically the theory of hypergraph rigidity, as a generalization of the usual Euclidean rigidity, and showed how it can be used to mirror several different theoretical problems, including tensor completion.