We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
1/2020
Towards finding hay in a haystack: explicit tensors of border rank greater than 2.02m in $\mathbb{C}^m\otimes \mathbb{C}^m\otimes \mathbb{C}^m$
We write down an explicit sequence of tensors in $\mathbb{C}^m\otimes\mathbb{C}^m\otimes\mathbb{C}^m$, for all m sufficiently large, having border rank at least 2.02m, overcoming a longstanding barrier. We obtain our lower bounds via the border substitution method.
