Geometry Seminar

Date: April 28, 2023

Time: 4:00PM - 5:00PM

Location: BLOC 302

Speaker: Derek Wu, TAMU

Title: Border rank bounds for GL_n-invariant tensors arising from spaces of matrices of constant rank

Abstract: 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.