Commutative Algebra Seminar

Title

Boij-Söderberg theory for Grassmannians

Abstract

Boij-Söderberg theory is a structure theory for syzygies of graded modules: a near-classification of the possible Betti tables of such modules (which record the degrees of generators in a minimal free resolution). One of the surprises of the theory was the discovery of a “dual” classification of sheaf cohomology tables on projective space.

I’ll tell part of this story, then describe some recent extensions of it to the setting of Grassmannians. Here, the algebraic side concerns modules over a polynomial ring in kn variables, thought of as the entries of a k x n matrix. The goal is to classify “GL_k-equivariant Betti tables” and relate them to sheaf cohomology tables on the Grassmannian Gr(k,n). This work is joint with Nic Ford and Steven Sam.