Secant v. Cactus

Border rank bounds for GLn-invariant tensors arising from spaces of matrices of constant rank

10 mai 2023, 16:00

1h

Building 1R3, Amphitheater Schwartz (Institut de Mathématiques de Toulouse)

Orateur

Derek Wu (Texas A&M University)

Description

One measure of the complexity of a tensor is its border rank.
Finding the border rank of a tensor, or even bounding it, is a difficult problem that is currently an area of active research, as several problems in theoretical computer science come down to determining the border ranks of certain tensors.
For a class of $GL(V)$-invariant tensors lying in a $GL(V)$-invariant space $V\otimes U\otimes W$, where $U$ and $W$ are $GL(V)$-modules, we can take advantage of $GL(V)$-invariance to find border rank bounds for these tensors.
I discuss a special case where these tensors correspond to spaces of matrices of constant rank.