3:45PM: Hypergraphic divisors, curves, and morphismsJenia TevelevThe birational geometry of the GrothendieckKnudson moduli space of stable rational curves is still largely a mystery. It is not known if the cone of effective divisors is polyhedral, if the cone of effective curves is generated by 1strata (Fulton's conjecture), if it has only finitely many small modifications, and so on. In a joint work with AnaMaria Castravet, we found out that some of this complexity can be explained by the fact that this moduli space can be interpreted as the BrillNoether locus of a bunch of very special reducible curves related to hypergraphs. Using this we constructed myriads of new extremal divisors and rigid curves.

5:00PM: Homological Dimension and the Continuum Hypothesis (after Osofsky)Nam Trang
