3:45PM: Syzygies of Koszul algebrasAldo ConcaKoszul algebras are certain algebras defined by quadratic relations; most quadratic algebras that arise naturally are in fact Koszul. There is no finite criterion for Koszulness, however, so it is interesting to study necessary or sufficiently conditions. I will explain what Koszul algebras are, and describe special features of their syzygies.

5:00PM: Toric Ideals of HypergraphsElizabeth GrossThe edge subring of a graph G is the monomial subalgbera parameterized by the edges of G. It’s defining ideal, commonly referred to as the toric ideal of G, has been wellstudied and several historical results tell us the same beautiful story: we can understand these ideals by understanding the combinatorics of the underlying graph. A natural extension is to consider the toric ideal of a hypergraph. In this talk, we will survey wellknown results on the toric ideals of graphs and explain how these concepts generalize to hypergraphs. We will end with recent results on the toric ideals of hypergraphs.
