Title: An old problem in linear algebra relevant for quantum information theory and complexity theory, and what modern algebraic geometry can tell us about it. 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. Such spaces have been studied for a long time, but little is known about them. I'll explain classical and modern results about them, and why people in complexity theory and quantum information theory care about them.
