Boij-Söderberg Theory for GrassmanniansAlgebra & Discrete Mathematics
|Speaker:||Jake Levinson, University of Michigan|
|Start time:||Mon, May 22 2017, 4:10PM|
Boij-Söderberg theory is a structure theory for syzygies of graded modules: a near-classification of the possible Betti tables of such modules (these tables record the degrees of generators in a minimal free resolution; the classification involves a simplicial complex built out of Young's lattice). 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 k*n variables, thought of as the entries of a k \times n matrix. The goal is to classify "GL_k-equivariant Betti tables", recording the syzygies of equivariant modules, and to relate them to sheaf cohomology tables on the Grassmannian Gr(k,n). This work is joint with Nic Ford and Steven Sam.