12 noon, Seminar Hall Toward a new way of computing GromovWitten invariants Robert Silversmith University of Michigan, Ann Arbor, USA. 250414 Abstract This will be an introductory talk about the "Amodel LandauGinzburg/CalabiYau correspondence." This is a (largely conjectural) correspondence between the GromovWitten theory of a CalabiYau manifold (or orbifold) and a new theory of Fan, Jarvis, and Ruan based on ideas by Witten. Roughly, the GromovWitten theory of a complex manifold X counts the number of holomorphic curves of a given degree and genus in X, satisfying some specified conditions. They are expressed as integrals over moduli spaces of stable maps. For example, the number 609250 of degree 2 curves on a quintic threefold, calculated by Kontsevich in the early 90s (and previously predicted by physicists), is a GromovWitten invariant. FanJarvisRuanWitten invariants are more subtle, and are expressed as integrals over covers of moduli spaces of stable curves. Since moduli spaces of curves are more wellunderstood than spaces of stable maps, these integrals should in theory be easier to compute directly than GromovWitten invariants. There is a wide conjecture with origins in physics that the two theories should be recoverable from each other. This was proven by Chiodo and Ruan for the special case of the quintic threefold in 4dimensional projective space, and some other examples have since been worked out. If I have time I will discuss basic computational evidence toward a generalization to a nonabelian orbifold.
