Spaces of matrices of bounded rank

Abstract: A classical problem in linear algebra is to understand what are the linear subspaces of the space of $m\times n$ matrices such that no matrix in the space has full rank. This problem has connections to theoretical computer science, more precisely complexity theory, and algebraic geometry. I will give a history, explain the connection to algebraic geometry (sheaves on projective space satisfying very special properties), and recent progress on the classification question. This is joint work with Hang Huang.

algebraic geometrynumber theory

Audience: researchers in the discipline

SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

We normally meet in-person in the indicated room. For online editions, we use Zoom and distribute the link through the mailing list. If you wish to be put on the mailing list, please subscribe to ntag-external using lists.sfu.ca