## Robin Hartshorne

An Ulrich bundle is a vector bundle on a projective variety \$X\$ that has no intermediate cohomology (called ACM bundle) and has the maximum number \$dr\$ of generators of the associated graded module, where \$d = \$degree of \$X\$ and \$r =\$ rank of bundle. We show the existence of stable Ulrich bundles of all ranks \$r \geq 2\$ on a nonsingular cubic surface in \$P^3\$, and of all even ranks \$= 2\$ on a nonsingular cubic threefold in \$P^4\$. (joint work with Marta Casanellas)}

## Cynthia Vinzant

Given a linear space L, we will find a universal Groebner basis and Hilbert series of the prime ideal I of polynomials vanishing on the coordinate-wise reciprocal of L. To do this, we'll degenerate this ideal into the Stanley-Reisner ideal of a broken circuit complex, which is a simplicial complex associated to the matroid of L. This talk will be following a paper of Proudfoot and Speyer (arXix:0410069).