Spaces of matrices of constant rank, vector bundles, and truncated graded modules

Abstract: A space of matrices of constant rank is a vector subspace V, say of dimension n+1, of the set of matrices
of size axb over a field k, such that any nonzero element of V has fixed rank r. It is a classical problem
to look for examples of such spaces of matrices, and to give relations among the possible values of the
parameters a,b,r,n. In this talk I will report on several joint projects with D. Faenzi, P. Lella, and E. Mezzetti, introducing new methods to classify and produce examples of such spaces.
The techniques that I will explain involve vector bundles on projective spaces, and in particular globally generated bundles and instanton bundles, as well as finitely generated graded modules over the ring of polynomials k[x_0,...,x_n].