Séminaire de Géométrie Complexe

Linear spaces of matrices of bounded rank

by Joseph M. Lansberg (Texas A&M University)

salle 207 bâtiment 1R2 (Institut de Mathématiques de Toulouse)

salle 207 bâtiment 1R2

Institut de Mathématiques de Toulouse

A linear subspace of a space of matrices is said to be of bounded rank r,
if every matrix in the space has rank at most r and some matrix has rank equal to r. The study of such spaces dates back at least to Marcus and Flanders in 1962. In 1997 Eisenbud and Harris observed that the question could be studied from the perspective of algebraic geometry.
I will describe very recent progress on this study with Hang (Amy) Huang
where we combine classical and algebreo-geometric techniques.
If time permits, I will explain our motivation from questions in theoretical computer science and quantum information theory.