Filtering Grassmanian Cohomology via $k$-Schur Functions

This talk concerns the cohomology rings of complex Grassmanni- ans. In 2003, Reiner and Tudose conjectured the form of the Hilbert series for certain subalgebras of these cohomology rings. We build on their work in two ways. First, we prove “half” of their conjecture, using notions from the theory of k-Schur functions. Second, we formulate an analogous conjecture for Lagrangian Grassmannians.