## Geometry Seminar

**Date: ** March 6, 2023

**Time: ** 3:00PM - 4:00PM

**Location: ** BLOC 302

**Speaker: **H. Huang, Auburn

**Title: ***New examples of basic vector spaces of matrices of low rank*

**Abstract: **A linear subspace of the space of bxc matrices is of bounded rank r if
no matrix in the space has rank greater than r. Classifications of such spaces is an interesting and important problem. The only cases known are when r \leq 3 with two proofs given by Artkinson via the study of Atkinson normal form and Eisenbud-Harris via the study of the first Chern class of a sheaf associated to the space. We will discuss a connection between these two approaches. Then we will discuss recent developments of this problem when r = 4 by linking it with the study of space of complexes of length 3.