3:45: Gorenstein liaison of varieties in projective space, recent results and questionsRobin HartshorneFor curves in projective 3-space (and more generally for subschemes of codimension 2 in any projective space) the theory of liaison has been enormously useful. In trying to generalize this theory to schemes of higher codimension it seems that Gorenstein liaison, rather than complete intersection liaison, is most likely to give analogous results. However, there are several different flavors of Gorenstein liaison, and many open problems. I will give a report on recent work. |
5:00: The level-rank duality for nonabelian theta functionsAlina MarianSpaces of sections of tensor powers of the theta line bundle on moduli spaces of semistable arbitrary rank bundles on a smooth curve are subject to a level-rank duality: each space of sections is geometrically isomorphic to the dual of the space of sections obtained by interchanging the tensor power (level) of the theta bundle on the moduli space and the rank of the bundles that make up the moduli space.I will describe a proof of this duality, which is the result of joint work with Dragos Oprea, and draws inspiration from work by Prakash Belkale who established the isomorphism for a generic curve. |