Oriol Reig: The cactus rank and structure tensors of Artinian Gorenstein algebras

Abstract: The study of the symmetric rank of symmetric tensors is deeply connected to zero dimensional schemes, Veronese embeddings and Artinian Gorenstein algebras. In this talk we will study the cactus rank of symmetric tensors, a nonreduced analog of the symmetric rank, from multiplication tensors of Artinian algebras. Within this perspective, we will recover the Bernardi–Taufer cactus algorithm and explore the characterization of symmetric multiplication tensors. This is a joint work with A. Bernardi and J. Jelisiejew.