3:45PM: Vector Bundles on P^n and Representations of GL_nDavid EisenbudBoijSoederberg theory can be thought of as saying that an arbitrary vector bundle on $P^n$ ``looks like" a certain homogeneous bundle (that is, one made from a representation of $GL_n$ applied to the tangent bundle). I will explain this connection, and a new application of the philosophy that leads to sharp statements about the vanishing of cohomology of tensor products of bundles on $P^n$. This is all joint work with Frank Schreyer.

5:00PM: Singularities of Cox Rings of Fano VarietiesMorgan BrownThe Cox Ring of an algebraic variety is a generalization of the homogeneous coordinate ring of a projective variety. I will give an introduction to Cox Rings and how they are used in birational geometry, as well as some ideas from the minimal model program, with the aim of showing that the Cox ring of a Fano variety over $\mathbb{C}$ is Gorenstein
