Seminar is on Wednesday in Padelford C-36 at 4:00pm-5:10pm.
Pre-seminar is on Wednesday in Padelford C-401 at 3:00pm-3:25pm.

Vector bundles of conformal blocks on $M_{g,n}$, the moduli space of stable $n$-pointed curves of genus $g$, are determined by a simple Lie algebra, a positive integer level, and an $n$-tuples of dominant integral weights. On $M_{0,n}$ the bundles are globally generated and their first Chern classes are base point free. The ranks of the bundles, for $\mathfrak{sl}_{r+1}$, can be computed using Schubert calculus. In this talk, using quantum Kostka and other tools, I classify ranks of $\mathfrak{sl}_{2m}$ bundles with so-called rectangular weights. Using similar techniques I show that the subcone of the nef cone spanned by the infinite family of first Chern classes of bundles of rank one is actually polyhedral, the convex hull of a finite number of extremal rays.